Bending, Crushing, and Connector Behavior of Pultruded ...

Graduate Theses, Dissertations, and Problem Reports

2012

Bending, Crushing, and Connector Behavior of Pultruded Glass Bending, Crushing, and Connector Behavior of Pultruded Glass

FRP Tubes FRP Tubes

Denny Wayne Dispennette West Virginia University

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Bending, Crushing, and Connector Behavior of Pultruded Glass FRP Tubes

Denny Wayne Dispennette

Thesis submitted to the Benjamin M. Statler College of Engineering and Mineral Resources at

West Virginia University in partial fulfillment of the requirements

for the degree of

Master of Science in

Civil Engineering

Approved by

Hota V. S. GangaRao, PhD, Chair P.V. Vijay, PhD

Mark Skidmore, PE

Department of Civil and Environmental Engineering

Morgantown, West Virginia 2012

Keywords: Glass FRP; composites; thin-wall; tube; bending stiffness; failure prediction

ABSTRACT

Bending, Crushing, and Connector Behavior of Pultruded Glass FRP Tubes

Denny Dispennette West Virginia University

Understanding the complex mechanics involved in the behavior of thin-walled fiber

reinforced polymer (FRP) composite tubes is essential for optimal structural applications. Flexural, crushing, and connection tests were performed on large-diameter thin-walled (D/t > 20) cylindrical tubes comprised of glass FRP composites manufactured using pultrusion process. The tubes were made of either a vinyl ester or a polyurethane matrix, using high pressure resin infusion during pultrusion.

Full scale bending tests were performed with 16 and 12 inch diameters spanning 320 and 240 inches, respectively. The test data revealed that the tubes possessed superior mechanical properties, with ultimate bending strengths of 50-70 ksi and elastic moduli ranging from 5.5-6.6 Msi. The failure mode from the full scale four point bending tests was determined to be crushing on the compression face coupled with local buckling. In addition, two types of connection tests were executed: a transverse bolt test and a washer test. The transverse bolt test exhibited maximum loads of 18-25 kips. The washer data ranged from 14-27 kips with failure occurring as local cracking. Coupon tests under tension, flexure, and compression were conducted after cutting them from full size tubes, resulting in maximum tensile stresses from 95-107 ksi. Also conducted on full scale specimens were four-point bending fatigue tests up to 200 cycles at 40% of the ultimate static bending stress and further tested to failure under static load conditions. The results revealed that polyurethane outperformed vinyl ester. The vinyl ester was shown to outperform in the transverse bolt test because of vinyl ester’s higher strength and stiffness under localized load conditions.

Investigation of the four-point bending results revealed a bilinear load versus strain response during loading. The bilinear response is shown to be caused by cross section deformation, aka, ovalization. This deformation was captured through video footage of the experiment and confirmed by finite element analysis. Application of classical lamination theory and finite element modeling was performed and found to under-predict the full scale bending stiffness in relation to experimental results. A failure prediction technique for the full scale four point bending is proposed that includes local buckling effect. A more direct approach proposed herein modifies the typical bending stress calculations by accounting for a local compression stress. Good agreement is found between the proposed technique and experimental data with errors ranging from 4-8%. This proposed technique is compared with the standard bending stress formulation and is shown to be more accurate, thus confirming the proposed approach’s ability to account for the local effects.

iii

ACKNOWLEDGEMENTS

I would like to first acknowledge my Lord and Savior Jesus Christ for extending to me great

mercy and grace that I am able to know Him and attempt to bring glory to Him through this

work. For laying down His life for me and redeeming me I am eternally grateful.

I also must thank my research advisor, Dr. Hota GangaRao who invited me to come to

WVU to pursue a Master’s degree program. Over the past two years, Dr. Hota has been available

at all times, and he has pushed me and instructed me with much wisdom and encouragement. I

will always be thankful for him being so patient and helpful with me.

I would like to thank Dr. Liang for guiding me through my previous research endeavor

which is not mentioned in this work, but which helped form the foundation for my research

skills. Also, I would like to thank Dr. Vijay for serving on my review committee.

I am also grateful for Dustin Troutman, director of product development at Creative

Pultrusions, who supported me with information and feedback regarding results.

I also thank Mark Skidmore for guiding me through all the mechanical testing and Jerry

Nestor for preparing testing fixtures and operating the equipment. Because the tubes tested were

so large and so many, I have to thank Bill Causey, Ken Donald, and Praveen Majjigapu for

providing assistance with testing. I am also grateful for David Dittenber for lending me books,

technical report advice, and for thinking through ideas with me.

Finally, I am appreciative of my family and friends, especially my local Church family for

being so encouraging during this time.

Financial support for this work has been provided by Creative Pultrusions, Inc.

iv

TABLE OF CONTENTS

ABSTRACT ................................................................................................................................... ii

ACKNOWLEDGEMENTS ........................................................................................................ iii

TABLE OF CONTENTS ............................................................................................................ iv

LIST OF FIGURES ................................................................................................................... viii

LIST OF TABLES ...................................................................................................................... xii

CHAPTER 1 INTRODUCTION ........................................................................................... 1

1.1 Background ..................................................................................................................... 1

1.2 Objectives ......................................................................................................................... 2

1.3 Organization of Thesis .................................................................................................... 3

CHAPTER 2 LITERATURE REVIEW ............................................................................... 5

2.1 Bending Behavior of Thin-Wall Tubes .......................................................................... 5

2.1.1 Seide and Weingarten ............................................................................................... 7

2.2 Plastic Bending Collapse of Metal Cylindrical Sections ............................................... 8

2.3 Prebuckling Response of Cylindrical Composite Tubes .............................................. 11

2.3.1 Tennyson Model ..................................................................................................... 12

2.3.2 Kedward Model ...................................................................................................... 13

2.3.3 Fuchs-Hyer Model .................................................................................................. 14

2.3.4 Ibrahim-Polyzois Model ......................................................................................... 16

2.4 Bending Stiffness Prediction of Composite Tubes ....................................................... 20

2.4.1 Stiffness Replacement Comparison ........................................................................ 21

2.4.2 Shadmehri-Derisi-Hoa Stiffness Model .................................................................. 24

2.4.3 Silvestre Generalized Beam Theory ....................................................................... 27

2.5 Conclusions ................................................................................................................... 28

CHAPTER 3 TESTING OF TUBE MEMBERS ............................................................... 30

3.1 Materials Tested ............................................................................................................ 30

3.2 Instrumentation ............................................................................................................. 31

3.3 Four-Point Bending ...................................................................................................... 32

3.3.1 Methodology ........................................................................................................... 32

3.3.2 Results and Discussion ........................................................................................... 34

3.4 Crush Testing ................................................................................................................ 50

3.4.1 Methodology ........................................................................................................... 50


3.5 Connection Testing A .................................................................................................... 61

3.5.1 Methodology ........................................................................................................... 61


3.6 Connection Testing B .................................................................................................... 66

3.6.1 Methodology ........................................................................................................... 66


3.7 Coupon Tests ................................................................................................................. 70

3.7.1 Tensile ..................................................................................................................... 70

3.7.2 Bending ................................................................................................................... 74

3.7.3 Compression ........................................................................................................... 77

3.8 Four-Point Bending Fatigue ........................................................................................ 80

3.8.1 Methodology ........................................................................................................... 80


3.9 Cantilever Bending Test ................................................................................................ 81

3.9.1 Methodology ........................................................................................................... 81


3.10 Conclusions ................................................................................................................ 83

CHAPTER 4 BENDING BEHAVIOR PREDICTION OF GFRP TUBES ..................... 86

4.1 Introduction and Scope ................................................................................................. 86

4.2 Analysis Methodology ................................................................................................... 86

4.3 Bending Stiffness Replacement - Laminated Plate Approach .................................... 95

4.4 Failure Load Prediction ................................................................................................ 98

4.5 Finite element Analysis ............................................................................................... 100

4.6 Conclusion ................................................................................................................... 105

CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS .................................... 108

5.1 Mechanical Testing of Glass FRP Tubes ................................................................... 108

5.1.1 Four-Point Bending Response .............................................................................. 108

5.1.2 Connection and Coupon Response ....................................................................... 109

5.1.3 Comparison of Polyurethane vs. Vinyl Ester ........................................................ 110

5.2 Theoretical Calculations ............................................................................................. 110

5.2.1 Theoretical vs. Experimental Data Comparison ................................................... 110

5.3 Recommendations ....................................................................................................... 111

REFERENCES .......................................................................................................................... 113

LIST OF FIGURES

Figure 2-1 Bifurcation Point for a Beam in Bending (Brazier, 1927) ............................................ 6

Figure 2-2 Curves showing moment-curvature characteristics of celluloid tubes (Brazier, 1927) 7

Figure 2-3 Ovalization of Tube due to Bending (Poonaya, Teeboonma, & Thinvongpituk, 2009)

....................................................................................................................................................... 10

Figure 2-4 Buckling Prediction Comparison (Fuchs & Hyer, 1996) ............................................ 16

Figure 2-5 Load-Deflection Relationship (Exp vs. FE) for Full-Scale Specimens (Ibrahim,

Polyzois, & Hassan, 2000) ............................................................................................................ 19

Figure 2-6 Load-Ovalization Relationship (Exp vs. FE) for Full-Scale Specimens (Ibrahim,

Polyzois, & Hassan, 2000) ............................................................................................................ 20

Figure 2-7 Plate Section of a Composite Tube Laminate (Chan & Demirhan, 2000) .................. 22

Figure 2-8 Shell Section of a Composite Tube Laminate ............................................................. 23

Figure 2-9 Applied Load vs. Axial Strain (mid-length bottom) of Tube 1 (Shadmehri, Derisi, &

Hoa, 2011)..................................................................................................................................... 27

Figure 3-1 Saddle for testing......................................................................................................... 33

Figure 3-2 Four-Point Bending Test (Section PU-16x0.5) ........................................................... 33

Figure 3-3 Strain Gage Diagram for Four-Point Bending Tests ................................................... 34

Figure 3-4 Failed Four-Point Bending Sample - Section PU-16x0.5 ........................................... 36

Figure 3-5 Stress vs. Strain for Sample 2 of Section PU-16x0.5 .................................................. 37

Figure 3-6 Stress vs. Strain for Sample 6 - Section PU-16x0.5 .................................................... 39

Figure 3-7 Stress vs. Strain for Sample 1 of Section VE-16x0.5 ................................................. 41

Figure 3-8 Stress vs. Strain for Sample 6 - Section VE-16x0.5 ................................................... 43

Figure 3-9 Failed Four-Point Bending Failure - Section PU-12x0.5 ............................................ 44

Figure 3-10 Stress vs. Strain for Sample 2 of Section PU-12x0.5 ................................................ 45

Figure 3-11 Stress vs. Strain for Sample 6 - Section PU-12x0.5 .................................................. 47

Figure 3-12 Failed Four-Point Bending Sample - Section PU-12x0.375 ..................................... 49

Figure 3-13 Stress vs. Strain for Sample 4 - Section PU-12x0.375 .............................................. 50

Figure 3-14 Crush Test Being Performed - Section PU-12x0.5 ................................................... 52

Figure 3-15 Crush Test Load vs. Deflection Response - Section PU-16x0.5............................... 54

Figure 3-16 Crush Test at Failure Load - Section PU-16x0.5 ...................................................... 55

Figure 3-17 Crust Test after Load was Released - Section PU-16x0.5 ........................................ 55

Figure 3-18 Crush Test Load vs. Deflection Response - Section VE-16x0.5 .............................. 57

Figure 3-19 Crush Test Load vs. Deflection Response - Section PU-12x0.5............................... 58

Figure 3-20 Crush Test Load vs. Deflection Response - Section PU-12x0.375........................... 60

Figure 3-21 Crust Test at Failure Load - Section PU-12x0.375 ................................................... 61

Figure 3-22 Connection Test A Setup .......................................................................................... 62

Figure 3-23 Connection Testing A at Failure - Section PU-16x0.5 ............................................. 63

Figure 3-24 Load/Deflection Plot of Connection Test A - Section PU-16x0.5 ............................ 64

Figure 3-25 Load/Deflection Plot of Connection Test A - Section VE-16x0.5 ............................ 65

Figure 3-26 Load/Deflection Plot of Connection Test A - Section PU-12x0.5 ............................ 66

Figure 3-27 Connection Test B Setup ........................................................................................... 67

Figure 3-28 Connection Test B Sample with 6-in Washer at 21 kip (failure) Load - Section PU-

16x0.5............................................................................................................................................ 69

Figure 3-29 Connection Test B Sample with 4-in Washer during Loading - Section PU-12x0.5 69

Figure 3-30 Tension Test Sample in Instron Machine.................................................................. 71

Figure 3-31 Failed Samples from Tensile Coupon Test ............................................................... 73

Figure 3-32 Coupon Tension Failed with Grips (Sample 16-4) ................................................... 74

Figure 3-33 Load/Deflection Response for Coupon Bending Tests - Section PU-12x0.375 ....... 76

Figure 3-34 Typical Failure for Coupon Bending Tests - Section PU-12x0.375 ......................... 77

Figure 3-35 Typical Failure for Coupon Compression Tests - Section PU-12x0.375 .................. 79

Figure 3-36 Cantilever Bending Test Setup.................................................................................. 82

Figure 4-1 Change in Stiffness Curve from Four-Point Bend Sample 6 (Tension Face) - Section

VE-16x0.5 ..................................................................................................................................... 87

Figure 4-2 Change in Stiffness Curve from Four-Point Bend Sample 6 (Compression Face) -

Section VE-16x0.5 ........................................................................................................................ 88


Section PU-16x0.5 ........................................................................................................................ 89


PU-16x0.5 ..................................................................................................................................... 89


Section PU-16x0.5 ........................................................................................................................ 90


Section PU-12x0.5 ........................................................................................................................ 92


PU-12x0.5 ..................................................................................................................................... 92


Section PU-12x0.375 .................................................................................................................... 93


PU-12x0.375 ................................................................................................................................. 94

Figure 4-10 Discretized Tube Modeled in ANSYS with External Loads and Boundary

Conditions ................................................................................................................................... 101

Figure 4-11 Load-Deflection Curve Comparison for Exp vs. FEM vs. CLT - Section PU-16x0.5

..................................................................................................................................................... 102

Figure 4-12 Load-Deflection Curve Comparison for Exp vs. FEM vs. CLT - Section VE-16x0.5

..................................................................................................................................................... 102


..................................................................................................................................................... 103

Figure 4-14 Load-Deflection Curve Comparison for Exp vs. FEM vs. CLT - Section PU-

12x0.375...................................................................................................................................... 103

Figure 4-15 Ovalization Comparison of Finite Results vs. Experimental Results ..................... 105

LIST OF TABLES

Table 2-1 Comparison of Ultimate Moments Predicted form Simplified Model and Test Results

(Poonaya, Teeboonma, & Thinvongpituk, 2009) ......................................................................... 11

Table 2-2 Curvature Effect on Bending Stiffness of Composite Tube with Ply Sequence of

[±452/02/±45]s (Chan & Demirhan, 2000) ................................................................................... 24

Table 2-3 Comparison of the Equivalent Bending Stiffness of the Composite Tube <EI>

(Shadmehri, Derisi, & Hoa, 2011) ................................................................................................ 26

Table 3-1 Material Sections Tested and Reported on ................................................................... 31

Table 3-2 Test Matrix ................................................................................................................... 31

Table 3-3 Four-Point Bending Results - Section PU-16x0.5 ........................................................ 36

Table 3-4 Four-Point Bending Results for Post-Fatigue Sample 6 - Section PU-16x0.5 ............. 38

Table 3-5 Four-Point Bending Results - Section VE-16x0.5 ....................................................... 40

Table 3-6 Four-Point Bending Results for Post-Fatigue Sample 6 - Section VE-16x0.5............. 42

Table 3-7 Four-Point Bending Results - Section PU-12x0.5 ........................................................ 44

Table 3-8 Four-Point Bending Results for Post-Fatigued Samples .............................................. 46

Table 3-9 Four-Point Bending Results - Section PU-12x0.375 .................................................... 48

Table 3-10 Crust Test Results - Section PU-16x0.5 ..................................................................... 53

Table 3-11 Crush Test Results - Section VE-16x0.5 .................................................................... 56

Table 3-12 Crush Test Results - Section PU-12x0.5 .................................................................... 58

Table 3-13 Crush Test Results – Section PU-12x0.375 ............................................................... 59

Table 3-14 Connection Test B Results - All Sections .................................................................. 68

Table 3-15 Coupon Static Tension Test Results - Section PU-16x0.5 ......................................... 71

Table 3-16 Coupon Static Tension Test Results - Section PU-12x0.5 ......................................... 72

Table 3-17 Coupon Static Tension Test Results - Section PU-12x0.375 ..................................... 72

Table 3-18 Coupon Bending Test Results - Section PU-12x0.375 .............................................. 76

Table 3-19 Coupon Compression Test Results - Section PU-12x0.375 ....................................... 78

Table 3-20 Four-Point Bending Fatigue Results .......................................................................... 81

Table 3-21 Cantilever Bending Test Results - Section PU-12x0.375 .......................................... 82

Table 4-1 Summary of Stiffness Change Points ........................................................................... 95

Table 4-2 Raw Material Properties used in Tube Sections ........................................................... 96

Table 4-3 Bending Stiffness Comparison, CLT vs. Experiment .................................................. 97

Table 4-4 Failure Load Prediction Compared to Experiment ....................................................... 99

1

CHAPTER 1 INTRODUCTION

1.1 Background

Over the past several years, fiber reinforced polymer (FRP) composites (two or more

constituents) have been proven to be a superior material when it comes to the aerospace,

automobile, and marine industries. An FRP composite is a material in which fibers and resin

bond together to form one solid material combining the properties of the constituent materials.

Fibers, typically glass or carbon, are the load carriers while the resin holds the fibers together and

transfers loads to the fiber network. The popularity of composites is due to a variety of reasons

including but not limited to: high strength to weight ratio, high energy absorption, and corrosion

resistance. For implementation into civil infrastructure, the ability of FRP to resist corrosion and

in turn have a long service life is paramount. Composite materials are being applied in a limited

manner as bridge decks, electrical transmission poles, and even bridge beams (Liang &

GangaRao, 2004). Cost per unit performance (i.e., bending load or deflection) of FRP

composites has decreased. As they have become more common, well established mass

manufacturing methods have been improved. Therefore, FRP composites are becoming viable

replacements for steel, concrete, or timber in many areas of civil application.

Composite materials are manufactured by different methods one of which is called

pultrusion. Pultrusion is a continuous composite manufacturing process that pulls fibers through

a resin bath. It is a low cost continuous mass manufacturing process because it quickly converts

fibers and resin into a finished composite (Barbero, 2011). Also, most pultrusion lines can run 24

hours a day. Appealing to civil applications, pultrusion offers the ability to produce many

2

different shapes of constant cross section with unlimited lengths. These shapes, for example, are

square/rectangular tubes, hollow cylindrical sections, and wide flanged beams.

As FRP sections come in with different dimensions, fiber architectures, and fiber-resin

combinations; hence their strength and stiffness limits must be tested experimentally. Large open

sections with relatively small wall thicknesses are known to fail under instability before reaching

their full strength capacity. Recognizing that engineers must be careful when designing and

predicting buckling behavior for isotropic materials, the problem becomes even more complex in

anisotropic materials. To properly design an anisotropic material based structural component,

experimental testing is absolutely necessary, especially for large diameter thin walled sections.

FRP composite members, such as cylindrical tubes, are not as well understood as their

equivalent metal sections. Because FRP composites have proven to be an advantageous option

when compared to conventional materials (e.g. steel) due to their higher strength to weight ratio

and corrosion resistance, extensive mechanical testing is necessary to exploit these benefits. The

bending stiffness and ultimate strength of composite tubes will be utilized extensively provided

they have designer friendly prediction equations for strength, stability, and stiffness.

Understanding crushing strength and connection behavior are essential to allowing for

composites to be used in a plethora of applications. Also the comparison of fiber-resin systems is

important in terms of their volume percent and determining the optimal fiber architecture and

geometric cross section.

1.2 Objectives

The objectives of this study for large diameter thin walled orthotropic tubular sections are:

3

• To review current theories for characterizing the failure mode of thin walled glass

FRP (GFRP) tubes in bending

• To determine bending, lateral crushing, and connection behavior in terms of stress

versus strain, deflection limits, crushing limits, and joint integrity of glass FRP

tubes

• To evaluate abilities of current prediction theories to match experimental results

1.3 Organization of Thesis

Chapter 2 provides a review of published literature on topics related to the experimental

objectives of this research. A brief review of the bending behavior of thin-walled structures is

presented. Then, aspects of composite materials are discussed, particularly bending behavior,

prebuckling response, and stiffness prediction of composite tubes.

Chapter 3 introduces the sections to be mechanically tested, and describes the differences of

each section. The experimental methodologies are covered in detail, and the results are reported

and analyzed. The tests conducted include full scale four-point bending tests, crush tests, two

types of connection tests, a variety of coupon tests, full scale four-point bending fatigue, and a

cantilever bending test of glass FRP composites. Direct comparisons are drawn between two

different resin systems.

Chapter 4 discusses in detail the bending behavior of the tubes tested in four-point bending from

Chapter 3. Further analysis reveals the change in bending stiffness throughout loading. A

standard prediction method is presented and the results are compared to experiment and finite

element analysis. Also presented is a method for determining the ultimate strength of the tubes in

bending. Comparisons to experimental results are presented.

4

Chapter 5 summarizes the results found in the previous chapters, draws general conclusions,

and provides recommendations for further work in this area of research.

5

CHAPTER 2 LITERATURE REVIEW

2.1 Bending Behavior of Thin-Wall Tubes

The study of the behavior of thin walled tubes of isotropic materials under bending has

been a concern for many years. Brazier’s work (1927) included higher order terms to account for

elastic stability and also to accurately describe the flexure problem for hollow specimens with

high moments of inertia. Brazier illustrated the principle of elastic stability of thin circular tubes

as a one dimensional cross section of a beam of small diameter (l/d = ∞). In this case, the

traditional methods of ignoring higher order terms in the bending problem, thus forming a linear

equation will not be accurate. Brazier (1927) notes, that in the case of pure bending, a maximum

moment is reached at a bifurcation point at which collapse is imminent. This is shown in Figure

2-1, where point A is the point of maximum moment. After this maximum moment the beam can

no longer resist higher moments and must collapse.

6

Figure 2-1 Bifurcation Point for a Beam in Bending (Brazier, 1927)

Introducing second order terms into St. Venant’s principle, Brazier derived the equation

curvature at which the maximum moment occurs for a thin cylindrical shell

𝑐2 =29

𝑡𝑅4(1 − 𝜎2)

(2-1)

at which point the maximum moment is

𝑀� =2√2

9𝐸𝜋𝑅𝑡2

√1 − 𝜎2. (2-2)

In Equations 2-1 and 2-2, c is the curvature, R is the radius, t is the wall thickness, σ is the

allowable stress, and E is Young’s modulus. Once the critical moment, 𝑀�, is reached, the

element of the tube in compression begins to deform leading to buckling. Brazier experimentally

7

confirmed his results in Figure 2-2 for long thin tubular beams made of celluloid and subjected to

pure end moments.

Figure 2-2 Curves showing moment-curvature characteristics of celluloid tubes (Brazier, 1927)

His theory matches well with the experimental data and has served as the foundation for

determining the mechanical behavior in thin-walled structures. It is important to remember when

looking at Brazier’s formulation that thin cylindrical tubes in consideration are infinitely long so

that end effects are not taken into account.

2.1.1 Seide and Weingarten

The relationship of critical bending stress and critical compressive stress was also studied

by Seide and Weingarten (1964). For several years prior to this study, the theoretical maximum

bending stress for buckling of a circular cylindrical shell was generally accepted as 1.3 times the

compressive buckling stress. Seide and Weingarten (1964) applied theoretical calculations using

Batdorf’s modification of Donnell’s equation for determining buckling loads of circular

cylinders. They considered combined compression and bending loading for shells with varying

8

R/t ratios and wave length. The results showed a ratio of critical bending stress to critical

compressive stress that varied widely with respect to R/t ratio. However, by minimizing the wave

length parameter the ratio of critical bending stress for buckling to compression buckling stress is

1 for all practical purposes in metals (Seide & Weingarten, 1964). Therefore the critical buckling

stress in bending is found from Equation 2-3

𝜎𝑐𝑟𝑖𝑡 = −2�𝐷11𝐸0𝑡

𝜌𝑡

(2-3)

where t is the wall thickness, E0 is the Young’s modulus in the circumferential direction, and ρ is

the local radius of the cylinder (from center to top of cylinder). This equation is for orthotropic

materials. Local buckling occurs when the maximum compressive stress reaches this value

(Seide & Weingarten, 1964).

2.2 Plastic Bending Collapse of Metal Cylindrical Sections

There have been many efforts to analyze the collapse behavior of thin walled circular tubes

in bending. Poonaya et al. (2009) presents a closed form solution for predicting the collapse

behavior for steel tubes subjected to pure bending. The collapse is divided into three phases: 1)

elastic phase, 2) ovalization phase, 3) structural collapse. The elastic phase was described as the

stage in which the material exhibits a linear stress-strain behavior. In the second phase (nonlinear

stress-strain), the cross section of the tube begins to deform into an oval shape, or ovalize. It is

assumed that the bending moment in this phase is constant and reached its ultimate value

(Poonaya, Teeboonma, & Thinvongpituk, 2009). The third phase is explained as the stage where

the load carrying capacity decreases rapidly due to local or global collapse in the section.

Collapse in this phase results in plastic hinge lines forming.

9

Understanding the behavior of the tubes in the second phase is paramount to predicting the

ultimate moment. Poonaya et al. (2009) reviewed two straightforward methods for determining

this ultimate bending moment as well as present their own method. The first method for finding

the ultimate bending moment, derived by Ueda (1985), is obtained by integrating the stress over

the cross section. His ultimate bending moment is:

𝑀𝑢 = 𝜎𝑦𝑍𝑝 + �𝜎𝑢 − 𝜎𝑦�𝑍𝑒 (2-4)

where σy is the yield stress, σu is the ultimate tensile stress, Zp = (4/3)(Ro3-Ri

3) is the plastic

bending section modulus, Ze = (π/4Ro)(Ro4-Ri

4) is the elastic bending section modulus, Ro is

the outer radius of tube, and Ri is the inner radius of tube.

By approximating the ovalized section as an elliptical shape, Elchalakani (2002)

produced an ultimate bending moment expression. From experimentation, it was displayed that

ovalization started once the major axis reached 1.10D and the minor axis reached 0.9D. Their

resulting expression is shown in the following equation:

𝑀𝑢 = 𝑆𝑜𝑣𝑎𝑙𝑖𝑧𝑒𝑑𝜎𝑦 =43

(𝑅𝑣2𝑅ℎ − 𝑅𝑣𝑖2 𝑅ℎ𝑖)𝜎𝑦 (2-5)

𝑅ℎ =𝐷ℎ2

= .55𝐷0

𝑅𝑣 =𝐷𝑣2

= .45𝐷0

where Sovalized is the plastic section modulus of an ovalized tube, σy is the measured yield stress

of an ovalized tube. Rh and Rv are the external horizontal and vertical radii of an ovalized tube,

respectively. The internal horizontal and vertical radii are Rhi = (Rh-t) and Rvi = (Rv-t),

respectively, and t is the thickness of tube (Elchalakani, Zhao, & Grzebieta, 2002).

10

Poonaya et al (2009) developed the two models described above into one method. This

ovalization model is shown in Figure 2-3.

Figure 2-3 Ovalization of Tube due to Bending (Poonaya, Teeboonma, & Thinvongpituk, 2009)

Using the radius of curvature R1, formed at the flattening ends of the cross section, and

assuming constant bending moment throughout the ovalization phase, and ignoring the rolling

hinge of the cross section, the ultimate moment of an ovalized tube can be found by integrating

the stress over the cross section. Assuming the geometry of the cross section to be inextensible,

the bending moment is expressed as

𝑀 = �𝜎𝑧𝑑𝐴𝐴

(2-6)

where dA = t ds is the cross-sectional area of an element of the tube, t is the thickness of the

tube, z is the distance from the neutral axis of a sectional ovalization to the circumferential area

and ds is the length of the circumferential cross section. After integrating Equation 2-6, and then

minimizing with respect to the deformation angle, φ, the ultimate bending moment is finally

obtained as

11

𝑀𝑢 = 3𝜎0𝑡𝑅2 (2-7)

where σ0 is the ultimate stress of material, t is the thickness of the tube, and R is the outside

radius of the tube.

Poonaya et al. (2009) sought to verify this formula by comparison with experimental

tests. Using steel specimens with known material properties and varying D/t ratios (21 to 43),

they set up an experiment that applied end moments to the specimen. The authors then compared

the results of their method, Ueda’s method, and Elchalakani’s method to the experimental

results. As shown in Table 2-1, the ultimate moment predicted by Poonaya et al. to correlate well

to experiment with slight overestimations for specimens with high D/t ratios.

Table 2-1 Comparison of Ultimate Moments Predicted form Simplified Model and Test Results (Poonaya, Teeboonma, & Thinvongpituk, 2009)

Poonaya et al.’s work presents a straightforward method for determining when

ovalization begins to occur in an isotropic cylindrical shell. The relation of this work to

laminated composites will be discussed later (Section 2.5) in this chapter.

2.3 Prebuckling Response of Cylindrical Composite Tubes

Ovalization describes the deformation of cylindrical cross sections subject to bending, and

is most notable in thin-walled structures. As described by Poonaya (2009) for isotropic materials

12

under bending, a cylinder goes through three phases: 1) linear elastic phase, 2) ovalization or

prebuckling state, and 3) a structural collapse phase. These three phases also occur in FRP

composite tubes. However due to the fibers typically used in composite materials, there is little

to no plastic region; therefore, the third phase isn’t marked by yield failure, but often abrupt

material failure. There are many factors that affect the local buckling of FRP composite tubes

such as: fiber type, matrix type, and fiber architecture/layup to name a few. The following papers

illustrated analyses performed on composite tubes that take into account these factors.

2.3.1 Tennyson Model

Tennyson (1971) found the critical moment for laminated anisotropic circular shells

based on the cylinder geometry and the material properties. The classical collapse moment can

be estimated from the theoretical axial compression buckling load for cylinders and is given as

𝑀𝑐𝑟𝑖𝑡 = 𝜋𝑅2𝑁𝑐𝑟 = 2𝜋𝑅�𝐸y𝑡𝐷11 (2-8)

where Ey is the Young’s modulus in the circumferential direction of the laminate, R is the radius

of the tube, and t is the wall thickness. Tennyson studied, furthermore, the effect of shape

imperfections on the buckling load for laminated composites. He concludes that the effects of

initial imperfection on the buckling load of composite cylindrical shells are similar to isotropic

shells. This research assumed a sufficient span length and therefore end effects were completely

ignored in this formulation.

Tennyson (1975) also conducted an extensive literature of the buckling of laminated

composite cylinders. For the cases of bending he cites a nonlinear prebuckling analysis for

various end constraints. Also, he cites the work of Cheng Ho (1963) in which bending critical

loads were found to be essentially equal to axial compression values; agreement with theory was

13

within 67%-90%. Tennyson also points out a work done by Jones (1969) that considers the

difference in elastic moduli for tension and compression. The assumption of constant elastic

moduli is generally made by designers; however, in the cases studied by Jones, one should be

aware of the difficulties associated with moduli differences in tension and compression

(Tennyson, 1975).

2.3.2 Kedward Model

Equations that are equivalent to Brazier’s work are deduced by Kedward (1978) for

laminated composites of any type of fiber and resin. He reviewed the assumptions made by

Brazier as 1) the shell is infinitely long, which removes the effects of end boundary conditions,

2) the deformation of the cross section with respect to the circumference is inextensional, and 3)

displacements in the tangential to circumference direction and then radial direction are always

small compared to the radius of the shell. He presented a collapse moment formula, Mcrit, a

moment-curvature relationship, M/ExI, and an equation for the reduction in vertical diameter, Δ.

Also, he presents these equations for the special case of the orthotropic shell:

𝑀𝑐𝑟𝑖𝑡 =2√2

9𝐸𝑥𝜋𝑅𝑡2

�1 − 𝜈𝑥𝑦𝜈𝑦𝑥�𝐸𝑦𝐸𝑥

(2-9)

𝑀𝐸𝑥𝐼

=1𝜌�1 −

32𝑅4

𝜌2𝑡2𝐸𝑥𝐸𝑦

(1 − 𝜈𝑥𝑦𝜈𝑦𝑥)� (2-10)

𝛥2𝑟

=𝑅4

𝜌2𝑡2(1 − 𝜈𝑥𝑦𝜈𝑦𝑥)

𝐸𝑥𝐸𝑦

(2-11)

where Ex is the Young’s modulus in the axial direction, Ey is the Young’s modulus in the

circumferential direction, R is the radius of the tube, t is the wall thickness, νxy and νyx are

Poission’s ratios, ρ is the radius of curvature of the tube axis, I is the moment of inertia of the

tube. Like the equation developed by Brazier, Equation 2-9 dictates when the tube will

14

experience collapse. It is at this point that the tube can no longer resist loading. Kedward also

notes that these equations are only concerned with local instability and the designer should

always be aware of general buckling when dealing with thin walled tubes (Kedward, 1978).

2.3.3 Fuchs-Hyer Model

Fuchs et al (1996) expanded Braziers work in order to determine the critical prebuckling

moment for short thin-walled composite cylinders in bending. Similar to Seide and Weingarten

mentioned above, Fuchs et al. employed Donnell’s shell theory to capture the geometric

nonlinearity. They outline a solution in which the applied end rotation is computed by integrating

Nx around the circumference at the end of the cylinder. This approach took into account

boundary condition effects, geometrically nonlinear deformations, and if desired, can include

initial imperfections and non-ideal boundary conditions (Fuchs & Hyer, 1996).

Fuchs et al. compared their predictions to the predictions found from the classical method

shown above in Equation 2-8 and the classical prediction found by Kedward (1978) shown in

Equation 2-12. Equation 2-12 is the precursor to Equation 2-8 which is for the special case of

orthotropy. This formula is an extension of the classical Brazier analysis to include constitutive

relations for balanced symmetric laminates. Their equation for the collapse moment results in

𝑀𝑐𝑟𝑖𝑡 = 2𝜋𝑅�8

27𝐸𝑥𝑡𝐷22

(2-12)

where Ex is the Young’s modulus in the longitudinal direction of the laminate, R is the radius of

the tube, and t is the thickness. End effects are completely ignored in this formulation. In both

classical equations shown above, the critical end rotation, Ωcri t, can be determined as

15

Ω𝑐𝑟𝑖𝑡 =𝑀𝑐𝑟𝑖𝑡𝐿2𝐸𝑥𝐼

(2-13)

where L is the span length, and I is the moment of inertia of the tube. Fuchs et al. test

three different layups and specimens of two different L/R ratios. Their results can be seen in

Figure 2-4.

16

Figure 2-4 Buckling Prediction Comparison (Fuchs & Hyer, 1996)

2.3.4 Ibrahim-Polyzois Model

The principles of critical buckling loads of thin-walled orthotropic cylinders were applied

by Ibrahim and Polyzois (1999) to characterize the prebuckling state, known as ovalization, of

FRP poles subjected to cantilever bending. The glass FRP poles studied in this work are to be

used as utility poles and they are tapered, decreasing in diameter from bottom to top, and are

17

manufactured by filament winding. Using finite element analysis and parametric full scale

mechanical testing, Ibrahim and Polyzois studied critical buckling in orthotropic members. Their

goal was to determine the effects of varying fiber layup on ovalization and to propose a

prediction equation based on Brazier’s work for the critical moments of thin-walled cylindrical

tubes. They proposed a design model for computing the critical ovalization load for FRP utility

poles. It includes the critical moment that can be carried by the pole and position where the

maximum ovalization occurs. The critical load applied in transverse direction to longitudinal

pole axis at the top of the pole for cantilever bending can be found by the following equation:

𝑃𝑐𝑟𝑖𝑡 =𝑀𝑐𝑟𝑖𝑡

(𝐿 − 𝑌) (2-14)

where L is the height of the pole measured from the loading position to the base. Mcrit and Y can

be found from the following expressions:

𝑀𝑐𝑟𝑖𝑡 = 2√2

9𝜋𝐸𝑥𝑅𝑡2

�1 − 𝜇𝑥𝑦2�2.1

𝐸𝑦𝐸𝑥

− .84 �𝐸𝑦𝐸𝑥�2

� (2-15)

𝑌 = �. 13− .04𝐸𝑦𝐸𝑥� �

𝑅𝑡

3𝐿 (2-16)

where Ex is the elastic modulus in the axial direction, Ey is the elastic modulus in the

circumferential direction, μxy is the poisons ratio of the laminate, R is the average radius of the

pole and t is the wall thickness.

Their results showed that increasing the number of circumferential layers increased the

critical ovalization load of FRP poles, and their proposed equation to determine critical

ovalization load matches well with their finite element results (Ibrahim & Polyzois, 1999).

Ibrahim and Polyzois’s equation for buckling cannot be taken as a broad stroke because

18

cantilever bending behavior does not encompass all of the same phenomena as pure bending

behavior. However, their findings can be adapted to further study the nonlinear ovalization

behavior of orthotropic beams in bending.

In a continuation of the previous study, Ibrahim et al. (2000) further discussed the

behavior of the composite tubes. The authors tested a variety of different layups in order to

optimize the most efficient fiber architecture and overall geometric dimensions for use as utility

poles. The researchers attempted to provide an ultimate strength prediction of the glass

composite utility poles using finite element methods. Their experimental setup was able to

capture the change in diameter of their specimens (tending to ovalize) under cantilever loading.

In the finite element model, the researchers employ an eight node quadrilateral shell element.

They also use a geometrical nonlinear model which uses the Newton-Rhapson iterative method

to incorporate shape changes into the stiffness equations during stepped loading. The researchers

predict failure in the model using the Tsai-Wu failure criteria unless local buckling was reached

before stress rupture (Ibrahim, Polyzois, & Hassan, 2000). A comparison of the load-deflection

results from experiment and finite element analysis is shown in Figure 2-5.

19

Figure 2-5 Load-Deflection Relationship (Exp vs. FE) for Full-Scale Specimens (Ibrahim, Polyzois, & Hassan, 2000)

It is also interesting to note the ovalization phenomenon under loading as well as the ability

of the finite element model to predict this phenomenon. These results are illustrated in Figure

2-6.

20

Figure 2-6 Load-Ovalization Relationship (Exp vs. FE) for Full-Scale Specimens (Ibrahim, Polyzois, & Hassan, 2000)

The authors go on to state that local buckling is the primary mode of failure for all the

tubes tested. Only one of the several tubes tested failed due to material failure and not local

buckling and this was due to that particular layup having no fibers in the circumferential

direction. The authors state that the presence of circumferential layers helps reducing ovalization

(Ibrahim, Polyzois, & Hassan, 2000). It should also be noted that a very similar work with

regards to finite element analysis of tapered composite utility poles having a service opening is

presented by Masmoudi et al. (2008). Their objective was to present an optimized GFRP section

to meet the design requires of utility poles (Masmoudi, Mohamed, & Metiche, 2008).

2.4 Bending Stiffness Prediction of Composite Tubes

The desire of many designers is to predict the overall bending stiffness of a laminated

composite section in order to analyze beams simply. This would be accomplished by using an

equivalent bending stiffness in formulas such as Euler-Bernoulli’s beam theory to predict

21

deflections and behavior of a composite section. The designer must always be aware that a

laminated composite cannot always be analyzed in the same fashion of an isotropic homogenous

material, and that any simplified equivalent stiffness does have the influence of many

assumptions.

The classical method of obtaining a bending stiffness for a composite tube involves

calculating the product of Young’s Modulus and moment of inertia of a FRP composite laminate

and assembling various laminates into a lamina over the circumference of a circular cross

section. This method is described by Kollár and Springer (2003) and presented in section 4.3.

To account for the many assumptions neglected by classical methods, non-classical

methods have been derived and are presented below as well.

2.4.1 Stiffness Replacement Comparison

There are a few different ways to predict the bending stiffness of a laminated composite

beam section. The most straightforward methods are classical approaches. The classical

lamination approach analyzes each ply layer individually and brings them together into an

overall stiffness matrix. When it comes to tube sections with a circular cross section, Chan et al.

(2000) present three approaches to determining the bending stiffness, EI.

The first is a smeared modulus approach. This approach uses the effective axial modulus

of the laminate and simply multiplies it by the moment of inertia of the tube section. The

expression is given as:

𝐸𝐼 = 𝐸𝑥𝜋4

(𝑅𝑜4 − 𝑅𝑖4) (2-17)

22

where Ex is the smeared modulus of the laminate obtained by lamination theory, and Ro and Ri

are the outer radius and inner radius of the tube, respectively.

The second approach is the laminated plate approach which considers an infinitesimal

plate section of tube laminate inclined at angle (see Figure 2-7).

Figure 2-7 Plate Section of a Composite Tube Laminate (Chan & Demirhan, 2000)

The overall stiffness matrices, [A] [B] [D], are computed as functions of angle θ, and are

then integrated accordingly. The affecting bending stiffness is then found expressed as

𝐷𝑥 =1�̅�11

(2-17)

where �̅�11is the (4,4) element of the inverse matrix of [�̅�𝐵�𝐷�] matrix (Chan & Demirhan,

2000).

θ

23

The third approach is the laminated shell approach which is similar to the laminated plate

approach; however, an infinitesimally small curved shell is considered instead of a plate (see

Figure 2-8).

Figure 2-8 Shell Section of a Composite Tube Laminate

Due to the curvature the derivation of the overall stiffness matrices is more complex, but

it follows the same fundamental procedure as used in the laminated plate approach.

Chan et al. (2000) use all three approaches for several tubes with a range of radii. They

compared each result to a finite element model based results, which they validated prior by

comparing to aluminum experimentation. The results of the stiffness prediction for the composite

tube are shown in Table 2-2. The percentage difference from the FEM solution is in parentheses

next to each stiffness value.

24

Table 2-2 Curvature Effect on Bending Stiffness of Composite Tube with Ply Sequence of [±452/02/±45]s (Chan & Demirhan, 2000)

As shown in Table 2-2, the shell approach yields the most accurate results, because the

shell approach considers a curved shell that is most similar to the tube. It’s also important to note

that the errors in results from each method increase as the radius of the tube decreases. This is

because the amount of curvature in the wall increases, and the smear approach and plate

approach suffer greatly as they do not take curvature into account in their derivation. It is the

shell approach that is comparable to the approach used in this paper (section 4.3) that is taken

from Kollár (2003).

2.4.2 Shadmehri-Derisi-Hoa Stiffness Model

Shadmehri et al. (2011) presented a non-classical formula for calculating the bending

stiffness of composite tubes. Their method was derived from a three-dimensional theory and

accounts for transverse shear deformation, non-uniform twist, and warping inhibition. The

equivalent stiffness is shown in their paper and the resulting equation involves laminate stiffness

coefficients from a three-dimensional [ABD] matrix which is too long to show here. This

equation is simplified for isotropic materials in the equation

25

⟨𝐸𝐼⟩ = 𝑅𝜋 �𝑅2𝐸𝑡

(1 + ν)(2ν − 1) �9ν3 + 3ν2 − 12ν + 4

4(2ν − 1)� +

𝑡3𝐸(ν − 1)12(1 + ν)(2ν − 1)�

(2-18)

where R is the radius of the tube, E is the Young’s Modulus, t is the thickness of the tube wall,

and ν is the Poisson’s ratio. The authors even provided a more simplified version by assuming ν

= 0.3 which is shown as

⟨𝐸𝐼⟩ = 𝐸 ∗ 𝑅3 ∗ 𝑡 ∗ 𝜋 �. 102 �𝑡𝑅�2

+ 1� (2-19)

The resulting stiffness is compared to a simplified moment of inertia approach which is

expressed as

⟨𝐸𝐼⟩ = �𝜋[(𝑅𝑜𝑛)4 − (𝑅𝑖4)4]

4𝐸𝑛

𝑁

𝑛=1

(2-20)

𝐸𝑛 =𝐴11𝐴12 − 𝐴122

𝐴22ℎ𝑛 (2-21)

where hn is the thickness of the particular layer group, n. This approach assumes symmetry. A

comparison of the non-classical method and the moment of inertia approach for varying layups is

presented in Table 2-3. The moment of inertia approach is calculated using Equation 2-20 and

the non-classical theory is found by the equation involving several terms containing laminate

stiffness coefficients which is not shown in this paper (Shadmehri, Derisi, & Hoa, 2011).

26

Table 2-3 Comparison of the Equivalent Bending Stiffness of the Composite Tube <EI> (Shadmehri, Derisi, & Hoa, 2011)

The researchers also compared their results to four experimental tests consisting of three

point bending and four point bending. Good agreement was found between the non-classical

prediction and experimental results, and the agreement is better than that of the moment of

inertia approach and experiment. A comparison of the non-classical theory and experiment for

tube 1 under three point bending is seen in Figure 2-9.

27

Figure 2-9 Applied Load vs. Axial Strain (mid-length bottom) of Tube 1 (Shadmehri, Derisi, & Hoa, 2011)

The results for all the tubes showed that good agreement is reached (Shadmehri, Derisi,

& Hoa, 2011). They also show that the moment of inertia approach works well only in the case

of cross ply tubes and not when fibers of other orientations are used (Shadmehri, Derisi, & Hoa,

2011).

2.4.3 Silvestre Generalized Beam Theory

Silvestre (2009) developed a generalized beam theory (GBT) for analyzing structural

behavior of laminate composite tubes. The author understands the many complexities of trying to

analyze a laminated composite structure and this proposed theory incorporates non-classical

effects including elastic material couplings, deformation of cross-section contour, warping

deformation, and shear deformation. Silvestre derives a GBT that includes these non-classical

effects and presents this derivation along with the results in his paper (Silvestre, 2009). Using a

finite element model to employ the resulting set of equations, Silvestre analyzes the linear (1st

order) behavior of two beam situations: (i) helically wound cantilevered tube under a tip load and

a (ii) clamped laminated short tube under a distributed load. He compares the GBT formulation

28

results for deformations at points along the circumference with the results obtained from shell

finite element analysis using ABAQUS. Fairly good agreement was shown for the two and the

discrepancies are explained in the paper. The GBT had a major advantage in that it uses far less

degrees of freedom than the shell finite analysis and produces a similar level of accuracy

(Silvestre, 2009). The research yields important information about the influence of shear and

material coupling effects on the linear behavior of composite circular hollow section tubes, and

goes to show that non-classical effects mentioned above must be incorporated into the analysis in

order to obtain accurate results (Silvestre, 2009). The author is currently extending this theory for

use in dynamic analysis and buckling analysis of FRP composite tubes.

2.5 Conclusions

During bending on of thin-walled isotropic tubes, warping of the cross section is shown to

precede buckling of the tube. The moment at which this occurred was first conveyed

mathematically by Brazier (1927) for the basic case of a long cylindrical shell in which end-

effects due to the load application were ignored. Seide and Weingarten (1964) attempted to

improve upon the understanding of the relationship of buckling stress during bending and

compressive buckling stress for thin-walled tubes and concurred that for all practical purposes

they can be considered to be equal.

For composite materials, the same buckling is known to occur; however, the factors that

cause/restrain buckling behavior are more complex due to factors such as: fiber type, matrix

type, fiber architecture/layup. Therefore a good ovalization prediction should take into account

the factors mentioned above. Tennyson (1971) and Kedward (1978) present moment predictions

that account for these factors. Ibrahim et al. (1999) modify Kedward’s model for cantilever

bending of composite utility poles and obtain good correlation with experimentation. These

29

simple models are classic in nature and do not account for nonlinearity; therefore, many

researchers have attempted to account for geometrical nonlinearity and also non-classical effects

such as boundary condition effects and initial imperfections. Fuchs et al. (1996) developed such

a theory and made several observations on the effect that non-classical conditions have on

prediction ovalization and critical moments. Silvestre (2009) also presented a generalized beam

theory in order to include non-classical effects such as elastic material couplings, cross section

deformation, warping deformation, and shear deformation. His results proved to be more

accurate compared to experimentation than the simplified methods commonly accepted by

engineers and designers. Also, an overall stiffness prediction is desirable for designers to easily

understand the material properties of a laminated composite. Classical methods explained by

Kollár et al. (2003) are described and utilized later in this paper. A good stiffness prediction for

laminated composite tubes will also account for non-classical effects such as elastic material

couplings, deformation of cross section contour, warping deformation, and shear deformation.

Silvestre’s (2009) GBT proves useful in this area too as it describes stiffness aspects of

composite tubes. Shadmehri et al. (2011) present a three-dimensional laminate theory to

determine a bending stiffness equivalent (EI) for composite tubes. Their approach is numerically

intensive and requires finite element analysis to employ, but the results prove more accurate

compared to experimentation than that of a moment of inertia approach which is commonly

accepted and simple to use.

30

CHAPTER 3 TESTING OF TUBE MEMBERS

3.1 Materials Tested

Creative Pultrusions Inc. provided WVU-CFC with tubes of circular sections for testing.

All sections were manufactured by the process of pultrusion. Four different types of circular

sections were tested: a 16” outer diameter ½” wall thickness E-glass/polyurethane, a 16” outer

diameter ½” wall thickness E-glass/vinyl ester, a 12” outer diameter ½” wall thickness E-

glass/polyurethane, and a 12” outer diameter 3/8” wall thickness E-glass/polyurethane. The

different sections are shown in Table 3-1. The nomenclature in this Table 3-1 will be used

throughout the report. Also, it is helpful to remember that the layup for each section is generally

the same and recognize that changes in diameter and wall thickness lead to slightly different

fabric layup. The tests done were four-point bending under static load to failure, four-point

bending fatigue, crush strength test, transverse bolt test (Connection Test A), washer test

(Connection Test B), and also various coupon testing of each section size and material. The

coupon level tests included testing for flexural properties (ASTM D790), compressive properties

(ASTM D695), and tensile properties (ASTM 638). A breakdown of the tests performed with the

exception of the coupon tests are shown in Table 3-2. The ASTM standards were used for

guidance for coupon tests and four-point full section bending, and the exact methodology used

for the tests are described below. The coupon samples were cut from the post-failure sections

used in the crush test.

31

Table 3-1 Material Sections Tested and Reported on

Section

Outside Diameter

(in)

Wall Thickness

(in)

Fiber Material

Matrix Material

PU-16x0.5 16 1/2 E-glass Polyurethane VE-16x0.5 16 1/2 E-glass Vinyl Ester PU-12x0.5 12 1/2 E-glass Polyurethane PU-12x0.375 12 3/8 E-glass Polyurethane

Table 3-2 Test Matrix

Number of tests Section 4pt Static

Bend Crush

Strength 4pt Fatigue

Bend Connection

A Connection

B PU-16x0.5 5 5 1 5 5 VE-16x0.5 5 4 1 5 6 PU-12x0.5 5 5 1 5 6

PU-12x0.375 4 3 0 0 0

3.2 Instrumentation

This section describes the necessary details of the data measurement devices generally

used throughout the experimental testing. In the methodology description for each experimental

setup, the particular instrumentation used will be noted. The devices used to record applied

loads, deflections, and strains are generally the same for each full section test, i.e. four-point

bending, crush, connection, and cantilever tests. For each full section test, loads were applied

through a hydraulic actuator controlled by an electric pump. The load transferred by the actuator

was measured with an Omega LC8400-200-200 load cell with ±0.5% accuracy. For all full

sections tests except connection test A, deflections were measured using a Celesco SP3 string pot

which has a maximum range of 50 inches and an accuracy of ±0.125 inches. For connection test

A, deflections were measured with an LVDT with an accuracy of 1/100th of an inch. Whenever

32

strain was recorded, a Vishay 250UW strain gage with 120 ohms resistance, ¼ inch gage length,

and a strain range of ±5% was used. The data acquisition system used to record all of these

measurements was a StrainSmart System 5000. Data points were recorded at a rate of 10 per

second in order to obtain detailed results.

3.3 Four-Point Bending

3.3.1 Methodology

The tests were conducted as per ASTM D6109 and WVU-CFC test protocol. The 12 inch

tubes were setup with a clear span of 240-inches out of a total length of 288-inches, with the load

span equal to 1/3rd of the clear span or 80-inches. The samples were supported and loaded by

using 8-inch long steel saddles that covered slightly less than half of the circumference as shown

in Figure 3-1. The 16 inch tubes were set up similarly with the clear span being 320 inches and

the load span equal to 1/3rd of the clear span or 106.67 inches. The saddles were loaded at the

midpoint through round steel stock to simulate simply supported conditions, and with neoprene

padding between the saddle and tube. Most tubes tested were instrumented with a Celesco SP3

string pot to measure deflections and an Omega LC8400-200-200 kip load cell. Vishay strain

gages were installed in the longitudinal direction, with additional gages on certain samples. The

load was transferred from a hydraulic actuator through the load cell and then to a steel spreader

beam, a W14x90 with transverse web stiffeners at loading points (Figure 3-2). The samples were

loaded to failure, and a few tests were recorded using an audio-visual system. Figure 3-2 shows

the four-point bending of a 16-inch sample, which is identical to the 12-inch testing except for

span length.

33

Figure 3-1 Saddle for testing

Figure 3-2 Four-Point Bending Test (Section PU-16x0.5)

All four-point bending samples had one strain gage at either the top of the cross section in

the longitudinal direction or at the bottom of the cross section in the longitudinal section, but

some samples had more gages on them. This was done to obtain strain data that occurs in other

locations of the cross section. Also, one sample from each section was fatigued and then tested to

failure under static loads (see section 3.8). These post-fatigued samples from each section set had

eight gages at the midspan. Figure 3-3 shows the possible locations for strain gages at the

34

midspan, and this figure will be referred to in further discussions as needed to highlight gage

locations.

Figure 3-3 Strain Gage Diagram for Four-Point Bending Tests

Also, for Sample 4 of PU-12x0.375 a video camera was setup facing the four-point

bending static test from the side so that the center span is in view. This was done in order to

monitor how much, if any, cross sectional deformation was occurring during bending. The

recorded footage is analyzed carefully to determine the change in diameter, and is presented in

section 4.5 (see Figure 4-15).

3.3.2 Results and Discussion

3.3.2.1 Introduction

As mentioned above, load, center deflection, and center longitudinal strain were recorded

(by instrumentation) under four-point bending. A few samples had more strain gages located at

35

the center also. A summary of the test results include max load, max deflection, max moment,

max stress (bending), max strain, and energy. All “max” measurements are taken at the max load

(load at failure). The moment, M, is calculated by Equation 3-1, where P is equal to the load at

one point of loading, and a is the distance from a point of loading to the nearest point of support.

𝑀 = 𝑃𝑎 (3-1)

The bending stress, σ, is calculated from Equation 3-2, where c is the distance from the

center of the cross section to the outermost fiber, and I is the moment of inertia.

𝜎 = 𝑀𝑐𝐼

(3-2)

The modulus of elasticity, E, is determined by fitting a linear curve through the linear

portion of the stress strain curve (within 10% - 50% of the ultimate strain). The energy is

computed by finding the area under the load deflection curve using an approximation technique.

The technique applied is a rectangular approximation, and it is found to be accurate due to the

many number of data points acquired during the test.

3.3.2.2 Section PU-16x0.5

The results from the four-point bending tests of the 16 inch Polyurethane samples are

given in Table 3-3. The moment is calculated using Equation 3-1. Crackling sounds were clearly

heard on all samples at around 75% of the failure load though no cracks were visible from a safe

viewing distance. Failure in all samples was sudden with the load dropping to zero in roughly 0.2

seconds. After failure, longitudinal cracks were found on the tube centered about midspan along

with crushing and tearing of the section at midspan. All samples failed in the middle third zone

36

of the test span as shown in Figure 3-4. Sample numbers refer only to the order in which they

were tested, and they are not sequenced between different test setups.

Table 3-3 Four-Point Bending Results - Section PU-16x0.5

Sample Max Load (kips)

Max Deflection

(in)

Max Moment (kip-in)

Max Stress (ksi)

Max Longitudinal

Strain (με)

Elastic Modulus

(Msi)

Energy (kip-in)

1 102.18 16.39 5446.31 59.53 11137 5.94 944.45 2 101.29 16.87 5398.85 59.01 11455 5.67 938.47 3 102.58 - 5467.41 59.76 11794 5.78 - 4 105.42 - 5619.05 61.42 10109 6.36 - 5 96.69 - 5153.59 56.33 11265 5.87 -

Average 101.63 16.63 5417 59.21 11152 5.92 941.46

Figure 3-4 Failed Four-Point Bending Sample - Section PU-16x0.5

After failure, all samples exhibited the combination of a compression crushing failure and

longitudinal cracks running along the length of the tube, which are indicative of a local buckling

failure (see Figure 3-4). Another reason to show that local buckling is contributing to failure is to

evaluate strain gage data. Sample 2 had a longitudinal strain gage located at the top (θ=0) and a

circumferential strain gage located on the side (θ=90), both at midspan. The stress vs. strain for

37

both strain gages is shown in Figure 3-5. Please note that a negative strain value indicates

compression and a positive strain indicates tension.

Figure 3-5 Stress vs. Strain for Sample 2 of Section PU-16x0.5

Figure 3-5 shows that the circumferential direction experienced a higher strain at the

failure stress of 59 ksi. Sample 5 which is not shown here also showed high strains at multiple

locations around the midspan in the circumferential direction; although, the top and bottom

longitudinal strains were never surpassed by the circumferential strains. Nevertheless, a

deformation of the cross section was occurring during loading of these samples and affecting the

failure mode, i.e. tension along circumference or buckling along longitudinal direction. More

confirmation of this effect is given in the results of the post fatigued sample.

One sample of PU-16x0.5 underwent 200 cycles of four-point bending at 40% of the

ultimate load (see Section 3.8). Afterwards, it was tested to failure in static four-point bending.

The static test results for this sample are shown in Table 3-4. Included with the sample’s results

is a comparison to the average values obtained from the static four-point bend tests given in

0

10

20

30

40

50

60

70

-15000 -10000 -5000 0 5000 10000 15000 20000

Stre

ss (k

si)

Strain (με)

Top Longitudinal

Side Circumferential

38

Table 3-4. This comparison is given as a percentage where a negative value conveys it was lower

than the average from the non-fatigued samples.

Table 3-4 Four-Point Bending Results for Post-Fatigue Sample 6 - Section PU-16x0.5

Sample

Max Load (kips)

Max Deflection

(in)

Max Moment (kip-in)

Max Stress (ksi)

Max Longitudinal Strain (με)

Elastic Modulus

(Msi) Energy (kip-in)

PU-16x0.5 Sample 6

103.72 - 5549 60.65 10372 5.76 -

Percent Difference from Static

Average

2.05 - 2.05 2.05 -6.99 -2.74 -

Results in Table 3-4 do not show any significant decrease in strength or stiffness.

Therefore, it is believed that the 200 cycles at 40% had no effect on strength or stiffness. Also,

for Sample 6 during the four-point bending test to failure, many gages were applied around the

circumference at midspan to further quantify any buckling behavior. Eight gages were applied in

the same locations and orientations for each section. Figure 3-3 shows the placement of these

gages. All of the possible locations and orientations in Figure 3-3 were used. The stress vs. strain

curve for PU-16x0.5 is shown in Figure 3-6.

39

Figure 3-6 Stress vs. Strain for Sample 6 - Section PU-16x0.5

The curves shown in Figure 3-6 illustrate important information about the behavior of the

circular pultruded FRP tubes. They confirm that in fact cross section deformation is occurring

and also give insight into when this deformation begins. It can be estimated from this data that

geometric nonlinearity begins at ~25-30 ksi which corresponds to 45-50% of the ultimate load.

This phenomenon will be discussed in further detail throughout the report.

3.3.2.3 Section VE-16x0.5

The results from the four-point bending tests of the 16 inch vinyl ester samples are given in

Table 3-5. Crackling sounds were not clearly heard on any samples until the applied load was

within roughly 95% of the failure load. No cracks were visible from a safe viewing distance until

failure. Failure of all samples was sudden and abrupt with the load dropping to zero in roughly

0.2 seconds. After failure, longitudinal cracks were found on the test specimen centered about

midspan along with crushing and tearing of the section at midspan. This material failed similarly

0

10

20

30

40

50

60

70

-15000 -10000 -5000 0 5000 10000 15000

Stre

ss (k

si)

Strain (με)

Top LongitudinalTop CircumferentialSide LongitudinalSide CircumferentialBottom LongitudinalBottom Circumferential45 Longitudinal45 Circumferential

40

to PU-16x0.5 (see Figure 3-4) for failure, but there were significantly less longitudinal cracks.

This indicates that stresses in circumferential direction affected the failure of VE-16x0.5 less

than PU-16x0.5. All samples failed at the center of the span with the exception of Sample 5

which failed beneath one of the loading saddles. Although neoprene padding was used between

the saddles, there is probably some digging of the saddle with the tube near failure loads. It

should be noted that the failure results from Sample 5 (Table 3-5) are very close to the average.

Sample numbers refer only to the order in which they were tested, and they are not sequenced

between different test setups.

Table 3-5 Four-Point Bending Results - Section VE-16x0.5


Max Deflection

(in)

Max Moment (kip-in)

Max Stress (ksi)


Elastic Modulus

(Msi)

Energy (kip-in)

1 87.41 13.85 4720.31 51.59 9891 5.66 687.45 2 64.53 9.77 3484.60 38.09 7136 5.54 340.97 3 86.70 12.98 4681.57 51.17 9311 5.43 624.76 4 90.31 13.27 4876.61 53.30 9461 5.45 667.60 5 86.35 - 4662.86 50.96 8763 5.80 -

Average 83.06 12.47 4485 49.02 8913 5.57 580.19

The failure mode of the samples of section VE-16x0.5 was less in the way of local

buckling when compared to PU-16x0.5. This is evident by the lack of longitudinal cracks at

failure and also the strain data acquired from Sample 1 of VE-16x0.5 which is shown in Figure

3-7. Please note that a negative strain indicates compression and a positive strain indicates

tension.

41

Figure 3-7 Stress vs. Strain for Sample 1 of Section VE-16x0.5

Figure 3-7 shows that the circumferential strain at the side of the sample was significantly

less than the longitudinal strain at the top. This does not mean that local buckling and cross

sectional warping were not occurring, but that it was less than that of the polyurethane

counterpart (see Figure 3-5). In fact local buckling was occurring some in this section, but

crushing in the compression zone is the primary mode of failure. More confirmation of this is

given in the stress vs. strain data recorded from the post fatigue sample.

One sample of section VE-16x0.5 underwent 200 cycles of four-point bending at 40% of

the ultimate load (see section 3.8). Afterwards, it was tested to failure in static four-point

bending. The static test results for this sample are shown in Table 3-6. Included with the

sample’s results is a comparison to the average values obtained from the static four-point bend

tests given in Table 3-6. This comparison is given as a percentage where a negative value

conveys it was lower than the average of the non-fatigued samples.

0

10

20

30

40

50

60

-12000 -10000 -8000 -6000 -4000 -2000 0 2000 4000 6000 8000

Stre

ss (k

si)

Strain (με)

Side Longitudinal

Side Circumferential

Top Longitudinal

42

Table 3-6 Four-Point Bending Results for Post-Fatigue Sample 6 - Section VE-16x0.5

Sample

Max Load (kips)

Max Deflection

(in)

Max Moment (kip-in)

Max Stress (ksi)


Elastic Modulus

(Msi)

Energy (kip-in)

VE-16x0.5 Sample 6

79.00 7.89 4227 46.20 7545 6.05 347.65


Average

-4.88 -36.72 -4.88 -4.88 -15.35 8.47 -40.08

Results in Table 3-6 do not show any significant decrease in stiffness. Therefore, it is

believed that the 200 cycles at 40% had no effect on stiffness. It is unclear whether the strength

was affected by the fatigue cycling or not. Although, according to Table 3-6, Sample 6 failed at a

much lower load and deflection than the average results from the non-fatigued samples, Sample

6 actually failed at the one of the points of load application as opposed to the center of the span.

This failure is the same as Sample 2 from the non-fatigued set (Table 3-5). Also, for Sample 6

during the four-point bending test to failure, many gages were applied around the circumference

at midspan to further quantify any buckling behavior. Figure 3-3 shows the placement of these

eight gages. All of the possible locations and orientations in Figure 3-3 were used. The stress vs.

strain curve for section VE-16x0.5 is shown in Figure 3-8.

43

Figure 3-8 Stress vs. Strain for Sample 6 - Section VE-16x0.5

The curves shown in Figure 3-8 give insight into the cross section distortion that occurs

throughout the bending test. Compared to its polyurethane counterpart (see Figure 3-6), section

VE-16x0.5 deformed less. The circumferential strain at the top (θ=0) is practically zero

throughout the duration of the test. It is difficult to say when exactly geometrical nonlinearity

begins for this section, but it appears to be at ~25-30 ksi bending stress which corresponds to 54-

65% of the ultimate stress.


The results from the four-point bending tests are given in Table 3-7. Crackling sounds

were clearly heard on all samples starting at around 75% of the failure load and continued

regularly until failure, though no cracks were visible from a safe viewing distance. Failure in all

samples was sudden and abrupt, though preceded by much crackling. After failure, longitudinal

cracks were found on the tube primarily centering about midspan along with crushing and tearing

0

5

10

15

20

25

30

35

40

45

50

-10000 -8000 -6000 -4000 -2000 0 2000 4000 6000 8000 10000

Stre

ss (k

si)

Strain (με)

Side CircumferentialTop CircumferentialBottom LongitudinalBottom Circumferential45 CircumferentialTop LongitudinalSide Longitudinal45 Longitudinal

44

of the section in the middle third zone of a test specimen. All samples failed in the middle third

zone of the test span as shown in Figure 3-9. However, some samples showed damage at one or

both points of loading due to load concentration. Sample numbers refer only to the order in

which they were tested, and they are not sequenced between different test setups.



Max Deflection

(in)

Max Moment (kip-in)

Max Stress (ksi)


Elastic Modulus

(Msi)

Energy (kip-in)

1 93.55 13.42 3741.93 75.04 13206 6.65 705.29 2 100.35 13.78 4014.06 80.50 13325 6.62 781.12 3 80.36 11.03 3214.50 64.46 9657 7.06 489.20 4 87.76 11.39 3510.38 70.40 11584 6.24 566.26 5 92.61 12.35 3704.33 74.29 15829 6.47 631.69

Average 90.93 12.39 3637 72.94 12720 6.61 634.71

Figure 3-9 Failed Four-Point Bending Failure - Section PU-12x0.5

45

The failure mode of these tubes is primarily crushing in the compressive face with some

attribution from local buckling; although less buckling is occurring than the direction 16 in

diameter counterpart. This is due to the PU-12x0.5 tube’s D/t ratio of 24 compared to the PU-

16x0.5 tube’s D/t ratio of 32. Sample 2 of section PU-12x0.5 had five gages located at varying

locations and orientations to quantify any local buckling. The stress vs. strain relationship for

Sample 2 is shown in Figure 3-10. Please note that a negative strain indicates compression and a

positive strain indicates tension.

Figure 3-10 Stress vs. Strain for Sample 2 of Section PU-12x0.5

Figure 3-10 shows the side circumferential approaching strain magnitudes close to both

the top and bottom longitudinal values indicating some cross sectional warping. It is also helpful

to see the top circumferential strain being highly nonlinear starting at around 35% of the failure

load. This shows when the local buckling is starting to begin. This also matches well with the

failure mode observed after the experiment. There were no longitudinal splits and the failure

0

10

20

30

40

50

60

70

80

90

-15000 -10000 -5000 0 5000 10000 15000

Stre

ss (k

si)

Strain (με)

Top LongitudinalTop CircumferentialSide CircumferentialBottom CircumferentialBottom Longitudinal

46

occurred mostly in the compressive zone as a result of local crushing/buckling (see Figure 3-9).

More confirmation of this is given in the stress vs. strain data recorded from the post fatigue

sample.

One sample of section PU-12x0.5 underwent 200 cycles of four-point bending at 40% of

the ultimate load (see section 3.8). Afterwards, it was tested to failure in static four-point

bending. The static test results for this sample are shown in Table 3-8. Included with the

sample’s results is a comparison to the average values obtained from the static four-point bend

tests given in Table 3-7. This comparison is given as a percentage where a negative value

conveys it was lower than the average from the non-fatigued samples.

Table 3-8 Four-Point Bending Results for Post-Fatigued Samples

Sample

Max Load (kips)

Max Deflection

(in)

Max Moment (kip-in)

Max Stress (ksi)


Elastic Modulus

(Msi)

Energy (kip-in)

PU-12x0.5 Sample 6

95.85 - 3834 76.89 12941 5.82 -


Average

5.41 - 5.41 5.41 1.74 -11.94 -

The results in Table 3-8 do not show any significant decrease in strength. Therefore, it is

believed that the 200 cycles at 40% had no effect on strength. It appears that there could have

been some decrease in stiffness due to the cyclic loading; however, more tests would need to be

done to confirm this. Also, for Sample 6 during the four-point bending test to failure, many

gages were applied around the circumference at midspan to further quantify any buckling

behavior. Figure 3-3 shows the placement of these gages. All of the possible locations and

47

orientations in Figure 3-3 were used. The stress vs. strain curve for section PU-12x0.5 is shown

in Figure 3-11.


The curves shown in Figure 3-11 illustrate that cross sectional deformation was even

occurring for section PU-12x0.5. The top and bottom of the cross section begin showing

nonlinear behavior at ~30-35 ksi bending stress which corresponds to 39-46% of the ultimate

stress.

3.3.2.5 Section PU-12x0.375

The results from the four-point bending tests are given in Table 3-9. Crackling sounds

were clearly heard on all samples starting around 80% of the failure load and continued regularly

until failure though no cracks were visible from a safe viewing distance. Failure in all samples

was sudden and abrupt, though preceded by much crackling. After failure, longitudinal cracks

were found on the tube primarily centering about midspan along with crushing and tearing of the

0

10

20

30

40

50

60

70

80

90

-15000 -10000 -5000 0 5000 10000 15000

Stre

ss (k

si)

Strain (με)

Top LongitudinalTop CircumferentialSide LongitudinalSide CircumferentialBottom LongitudinalBottom Circumferential45 Longitudinal45 Circumferential

48

section in the middle third zone of a test specimen. Most samples failed in the middle third zone

of the test span as shown in Figure 3-12. However, some samples showed damage at one or both

points of loading due to load concentration. Sample 4 underwent a cantilever bending test (see

section 3.9) up to ~33% of its projected ultimate strain prior to bending testing in static bending.

It is clear by the results of shown in Table 3-9, that these tests did not have any effect on the

ultimate strength or stiffness of the specimen. Sample numbers refer only to the order in which

they were tested, and they are not sequenced between different test setups.



Max Deflection

(in)

Max Moment (kip-in)

Max Stress (ksi)


Elastic Modulus

(Msi)

Energy (kip-in)

1 52.93 11.16 2117.39 54.86 10989 5.10 316.95 2 52.72 11.19 2108.62 54.63 10772 5.20 331.88 3 55.35 11.93 2213.88 57.36 10718 5.47 375.33 4 50.92 11.74 2036.61 52.76 10894 5.02 333.70

Average 52.98 11.51 2119.12 54.90 10843 5.20 339.46

49

Figure 3-12 Failed Four-Point Bending Sample - Section PU-12x0.375

Crushing on the compression face was the primary mode of failure for these sections, and

it appears to have been contributed to by local buckling behavior. As shown in Figure 3-12, the

failure was explosive and resulted in cracks forming in longitudinal and circumferential

directions. This was typical for all samples. Section PU-12x0.375 has a D/t ratio of 32 which is

the same as both 16 in diameter sections, and the same fiber-resin system as PU-16x0.5;

therefore, it was expected to have similar failure behavior. Also, for Sample 4 during the four-

point bending test to failure, many gages were applied around the circumference at midspan to

further quantify any buckling behavior. Figure 3-3 shows the placement of these gages. All of

the possible locations and orientations in Figure 3-3 were used. The stress vs. strain curve for

section PU-12x0.375 is shown in Figure 3-13.

50


The curves shown in Figure 3-13 give insight into the cross section distortion that occured

throughout the bending test. The circumferential strain at the top (θ=0°) and the circumferential

strain on the side (θ=90°) begin to behavior nonlinearly at ~15-20 ksi which corresponds to 27-

36% of the ultimate stress.

3.4 Crush Testing

3.4.1 Methodology

The “crush test” is a test that uses a reinforced square block, or “wale section”, to press

under point load on the tube section laterally (see Figure 3-14). The four-point bending tests led

to the failure in the middle (mostly) of the tubes, with the ends showing no signs of distress after

testing to failure. Therefore for sections PU-16x0.5, VE-16x0.5, and PU-12x0.5 the tested tubes

were cut near the ends to harvest undamaged ends so that they can be used for crush testing. For

0

10

20

30

40

50

60

-15000 -10000 -5000 0 5000 10000 15000

Stre

ss (k

si)

Strain (με)

Top LongitudinalTop Circumferential45 Longitudinal45 CircumferentialSide LongitudinalSide CircumferentialBottom LongitudinalBottom Circumferential

51

section PU-12x0.375, undamaged 60” samples were provided by CP. The samples were set in

the same saddles used in the four-point bend test with the rollers under the saddles removed. For

the 16-inch tubes, the saddles were set at 6-feet apart and the damaged end from four-point

testing was left to hang off the end, supported by a gantry crane to keep the specimen level. For

the 12-inch tubes, 4-foot sections of the tubes were cut from the undamaged ends and set in the

saddles, with the saddles supporting roughly 4 inches at each end of the tube as shown in Figure

3-14. For each test, the area between the saddles under the tube was fully supported

longitudinally on solid steel plates with a neoprene pad between the steel support plate and the

FRP composite. Load was transferred from a hydraulic actuator through a steel plate to an

Omega LC-8400-200-200 kip load cell and then through another plate into a 10-inch by 10-inch

solid polymer wale section that was supplied by CP (see Figure 3-14). The wale section was

connected to the steel plates by threaded rods for stability during testing. Deflection readings

were taken from the overhang of the wale section by a Celesco SP3 string pot. This position for

the deflection measurement was practically ideal; however, the readings will only show the

deflection of one side which could be more or less than the other side. This is due to loading

through a square wale section against the tube; therefore, it is difficult to maintain perfect

balance during loading. All test samples were loaded until the area around the application of the

load (i.e. top of the tube) failed to the point at which the section was no longer circular and the

wale section was nearly touching the sides of the tube (see Figure 3-16). Testing was stopped

before the sides were loaded as this caused damage to the wale section (cutting into surface of

wale section) and additional loading would simply crush flat the already failed structural system.

52

Figure 3-14 Crush Test Being Performed - Section PU-12x0.5



The results from the crush testing are given in Table 3-10 and Figure 3-15. Typically

there was little deflection induced under vertical loading until the specimen started cracking, then

deflection started to grow quickly. After around 2 inches of deflection, the top of the tube had

flattened out and longitudinal cracks were visible on both sides as shown in Figure 3-16, which

shows a tube under full load. Upon releasing the load, the tube returned to a circular shape as

shown in Figure 3-17. It should be noted that the ends of the tubes remained circular, and no

boundary effects were visible from the steel saddles. The string pot used to measure deflection

did not work properly for Sample 4, so no deflection readings were measured. To further

investigate if the failure load was peaked when the top flattened out, Sample 2 was loaded

beyond the failure load. As shown in Figure 3-15, after Sample 2 passed the reported maximum

Load Applied

53

load of 28.29 kips at 2.28 inches, the load maintained a plateau until approximately 3 inches.

This approximately corresponds to the location of the longitudinal cracks as seen in Figure 3-16

Figure 3-17. At this point, the load was being primarily supported by the vertical faces of the

tube which resulted in the tube cutting into the wale section slightly at these locations. Any

further loading would simply crush the sample flat and would not accurately demonstrate its

strength. Sample numbers refer only to the order in which they were tested, and they are not

sequenced between different test setups.

Table 3-10 Crust Test Results - Section PU-16x0.5


Deflection at Max

Load (in)

1 28.40 1.54 2 29.29 2.28 3 24.86 2.22 4 24.59 N/A 5 30.50 2.04

Average 27.53 2.02

54

Figure 3-15 Crush Test Load vs. Deflection Response - Section PU-16x0.5

Looking at Figure 3-15, each sample experiences a significant crack at ~0.5 inches of

deflection which was audibly heard. Another significant crack occurred at ~1.5 for each sample,

but the highest load attained for each sample immediately precedes the most significant damage,

cracks occurring on the sides of the sample, which seemed to happen at ~2-2.25 inches of

deflection. The load-deflection result for Samples 1, 2 and 5 do not start deflecting until high

loads, and this is due to an imbalance of the square section on the tube and deflection only being

measured on one side.

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5 3 3.5

Load

(kip

s)

Deflection (in)

Sample 1

Sample 2

Sample 3

Sample 5

55

Figure 3-16 Crush Test at Failure Load - Section PU-16x0.5

Figure 3-17 Crust Test after Load was Released - Section PU-16x0.5


The results from section VE-16x0.5 are very similar to those of section PU-16x0.5. As

noted above when the loading block reaches the sides of the cylinder it can take more load, but

56

this was not allowed to happen during these samples. Table 3-11 provides maximum load per

sample and deflections for all 4 test samples. It is noted that the vinyl ester samples failed at

lower loads than polyurethane samples and deflected less. However, Figure 3-18 which reveals

the energy absorption and ductility from the load versus deflection results. Each steep drop in

loading indicates a cracking/failing of the section, perhaps on a layer-by-layer basis. Sample

numbers refer only to the order in which they were tested, and they are not sequenced between

different test setups.

Table 3-11 Crush Test Results - Section VE-16x0.5


Deflection at Max

Load (in) 1 15.34 1.25 2 21.03 2.33 3 22.04 1.53 4 16.58 1.78

Average 18.75 1.72

57

Figure 3-18 Crush Test Load vs. Deflection Response - Section VE-16x0.5

As explained for section PU-16x0.5, crackling was audible and damage was occurring at

around ~0.5 inches deflection and up until the most significant damage which occurs at ~1.75

inches of deflection. It is at this deflection at which the wall of the tube showed a significant

crack along the side of the tube.


The results from the crush testing are given in Table 3-12 and Figure 3-19. Little

deflection occurred with the increase in loading until the specimen started crackling, then

deflection started to increase quickly. After 2 inches of deflection, the top of the tube had

flattened out and longitudinal cracks were visible on both sides, which show the tube under full

failure load on the tube (see Figure 3-16). Upon releasing the load, the tube returned to its

original circular shape. It should be noted that the ends of the tubes remained near circular in

cross section, and no reinforcement effects were visible from the saddles. Sample numbers refer

only to the order in which they were tested, and they are not sequenced between different test

setups.

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5

Load

(kip

s)

Deflection (in)

Sample 1Sample 2Sample 3Sample 4

58

Table 3-12 Crush Test Results - Section PU-12x0.5


Deflection at Max

Load (in) 1 28.05 1.52 2 26.77 1.42 3 25.98 1.3 4 27.91 0.62 5 29.02 1.08

Average 27.54 1.19


Looking at Figure 3-19, each sample experiences a significant crack at ~0.5 inches of

deflection which was audibly heard. Continued crackling is heard on the sample until the highest

load is attained for each sample which immediately precedes the most significant damage, cracks

occurring on the sides of the sample, which seems to happen at ~1-1.5 inches of deflection. The

load-deflection result for Samples 4 and 5 do not start deflecting until high loads, and this is due

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5 3

Load

(kip

s)

Deflection (in)

Sample 1Sample 2Sample 3Sample 4Sample 5

59

to an imbalance of the square section on the tube and deflection only being measured on one

side. This also explains why these two samples experienced the most major damage at a lower

deflection. It cannot be said which samples were most accurate with the deflection readings, but

this data provides a good range and a general approximation of failure load and deflection at

failure.

3.4.2.4 Section PU-12x0.375

The results from the crush testing are given in Table 3-13 and Figure 3-20. Little deflection

occurred with the increase in loading until the specimen started crackling, then deflection started

to increase quickly. After 2 inches of deflection, the top of the tube had flattened out and

longitudinal cracks were visible on both sides. Figure 3-21 shows the tube failure but with full

failure load on the tube. Upon releasing the load, the tube returned to a circular shape. It should

be noted that the ends of the tubes remained near circular in cross section, and no reinforcement

effects were visible from the saddles. Sample numbers refer only to the order in which they were

tested, and they are not sequenced between different test setups.

Table 3-13 Crush Test Results – Section PU-12x0.375


Deflection at Max

Load (in) 1 17.16 2.10 2 17.33 2.07 3 20.59 2.02

Average 18.36 2.06

60


Looking at Figure 3-20, each sample experienced a significant crack at ~0.5 inches of

deflection which was audibly heard. Continued crackling was heard on the sample until the

highest load was attained for each sample which immediately preceded the most significant

damage, cracks occurring on the sides of the sample, which seemed to happen at ~2 inches of

deflection.

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5 3 3.5

Load

(kip

s)

Deflection (in)

Sample 1

Sample 2

Sample 3

61

Figure 3-21 Crust Test at Failure Load - Section PU-12x0.375

3.5 Connection Testing A

3.5.1 Methodology

The purpose of this test was to simulate the effect of a load being applied to a bolt that

connects tubes together in a mooring pile situation. The goal is to determine the mode of failure,

the failure load, and to compare the tested sections to each other. A 1” diameter steel pin was

inserted through the middle of the 16” and 12” diameter tubes (see Figure 3-1 and Figure 3-22).

The holes for the pins were prepared by drilling through the material. Each tube length was

roughly 24”. The load was applied through the 1” diameter pin as shown in Figure 3-22. The

load versus deflection of the pin was recorded at each point that it touched the pipe as shown in

Figure 3-22. Two LVDTs were used directly under the pin on the outside of the load frame (see

Figure 3-22). This positioning yielded accurate deflections and conveys how much the pin hole

enlarged during loading to failure. Each specimen with the exception of first few Samples (1-3)

62

was loaded until the frame was about to be in contact with the top of the pipe; this was done in

order to obtain a good load-deflection curve with many points beyond the maximum load

resistance offered by the tube.

Figure 3-22 Connection Test A Setup


3.5.2.1 Introduction

For each section tested, similar types of load and deflection results were found. Although

the maximum loads differ for each section, the behavior was always the same. Eventually the

load would not go any higher because the pin deflection was steadily increasing. As opposed to a

LVDT Located Here – Left

LVDT Located Here (same as left)– Right

Deflection

Load Applied

Solid Support Along Length of

Specimen

1” diameter

63

catastrophic failure characterized by global cracking and delamination as seen in the bending and

crush tests, this type of loading seemed to push its way through the material locally (See Figure

3-23), i.e., large ductility was noted after initial cracking. It is difficult to quantify a maximum or

failure load because the pin just pushed its way through the material as the loading was

sustained. Therefore the maximum load is considered as the point where load stops increasing

and deflection continues to increase.

Figure 3-23 Connection Testing A at Failure - Section PU-16x0.5

Samples 1-3 were not loaded as far as others because of setup uncertainties. Right

deflection in Sample 4 also had an error at about 0.58 inches, but every sample tested after

Samples 1-4 was without error.


The load vs. deflection curve is shown in Figure 3-24. It can be seen that the maximum

load occurs whenever the load cannot increase anymore and deflection continues to increase.

Thus the max load is ~18-21 kips. Sample 1 is not shown because the LVDTs were not working

properly and the load was terminated before failure. Samples 1-3 were not loaded as far as others

64

because of setup uncertainties. Deflection on one side of Sample 4 also had a deflection error at

about 0.58 inches due to a snag in the LVDT wire, but every sample tested after Samples 1-4 was

without error. The results from this test, i.e. max load and stiffness, reveal the properties of the

resin system.

Figure 3-24 Load/Deflection Plot of Connection Test A - Section VE-16x0.5


The load deflection curve is show in Figure 3-25. It can be seen that the maximum load is

identified as the load that cannot increase anymore, while deflection continues to increase. Thus

the max load is ~23-25 kips. This maximum load is slightly higher than that of VE-16x0.5,

revealing that the polyurethane resin system is superior in terms of ultimate strength with regards

to local bolt loading.

0

5000

10000

15000

20000

25000

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Load

(lbs

)

Deflection (in)

Sample2 - Left Sample2 - RightSample3 - Left Sample3 - RightSample4 - Left Sample4 - RightSample5 - Left Sample5 - Right

65

Figure 3-25 Load/Deflection Plot of Connection Test A - Section PU-16x0.5


The load deflection curve is shown in Figure 3-26. It can be seen that the maximum load is

identified as the load that cannot increase anymore, while deflection continues to increase. Thus

the max load is ~21-23 kips. The maximum load reached by PU-12x0.5 is near that of PU-

16x0.5 which is to be expected since the only difference in the tubes is diameter. The minor

differences can probably be attributed to a difference in diameter which might allow the

transverse bolt to bend more in the case of a longer diameter tube.

0

5000

10000

15000

20000

25000

30000

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Load

(lbs

)

Deflection (in)

Sample6 - Left Sample6 - RightSample7 - Left Sample7 - RightSample8 - Left Sample8 - RightSample9 - Left Sample9 - RightSample10 - Left Sample10 - Right

66

Figure 3-26 Load/Deflection Plot of Connection Test A - Section PU-12x0.5

3.6 Connection Testing B

3.6.1 Methodology

This investigation includes the testing of two different sized washers. This was done in

order to determine the optimal size washer to be used for connections. The optimal sized washer

will protect the tube from as much damage as possible due to a direct load. A bolt hole of 1 inch

diameter was drilled straight through sections of the samples (same as Connection Test A). In

this test however, a bolt and a washer that were provided by Creative Pultrusions Inc. were

placed in the hole (See Figure 3-27). Two different sizes of washers were tested on test samples

with three repetitions, except only two repetitions were performed for the 16 inch polyurethane

pipe with a 6 inch washer. A 4” x 4” washer and a 6” x 6” were used, and these washers were

curved to the fit the tubes better (See Figure 3-27). The span lengths used for the 12” and 16”

0

5000

10000

15000

20000

25000

30000

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Load

(lbs

)

Deflection (in)

Sample11 - Left Sample11 - RightSample12 - Left Sample12 - RightSample13 - Left Sample13 - RightSample14 - Left Sample14 - RightSample15 - Left Sample15 - Right

67

diameter samples were 5’ and 6’ respectively. In all test specimens, 6 inches of overhang was

provided beyond the support. Load was measured with an Omega LC-8400-200-200 kip load

cell.

Figure 3-27 Connection Test B Setup


The failure behavior of the washer testing was found to be local depression around the

area of the washer and the washer itself deformed greatly until the load application tools were

flat against the test samples (Figure 3-28 and Figure 3-29). Loading was taken up to about the

same point on each sample after initial crack failure was witnessed. The results for all the

sections tested are given in Table 3-14.

68

Table 3-14 Connection Test B Results - All Sections

Section Washer Size (in)

Sample (ID #)

Max Load (lbs)

Average Max Load

(lbs)

PU-16x0.5 72 inch

span

4x4 1 16,402

17,210 2 17,540 3 17,688

6x6 1 23,230 22,228 2 21,226

VE-16x0.5 72 inch

span

4x4 1 13,161

14,291 2 15,115 3 14,596

6x6 1 17,738

17,837 2 18,851 3 16,921

PU-12x0.5 60 inch

span

4x4 1 21,275

19,569 2 17,985 3 19,445

6x6 1 24,219

27,642 2 24,120 3 34,585

The values in Table 3-14 show the maximum load at initial cracking failure. As seen in

Figure 3-28, the 6 in washer eventually dug into the FRP material and created cracks that

propagated along a significant longitudinal distance from the washer. The 6 in washers generally

caused less local damage to the sample at equal loads when compared to the 4 in washer. The

washer testing results had similar cracking and failure modes on all sections and even all

washers; however, the 4 inch washer would create a more local depression and generally caused

more local damage (Figure 3-29).

69

Figure 3-28 Connection Test B Sample with 6-in Washer at 21 kip (failure) Load - Section PU-16x0.5

Figure 3-29 Connection Test B Sample with 4-in Washer during Loading - Section PU-12x0.5

70

3.7 Coupon Tests

The purpose of coupon testing is to obtain properties of the material for comparison to the

material properties found from full section tests. Manufacturers who test coupon samples can use

the correlations presented in this work to determine the general behavior of a full section FRP

tube. The coupon samples were cut from the failed samples from the crush testing. The ends of

these failed sections do not appear to have any damage; however, such inference is made from a

visual inspection of coupons. It is not truly known if there was any internal damage. Samples

were cut first using a handheld circular saw and then were cut to size using a table saw with both

having a diamond blade.

3.7.1 Tensile

3.7.1.1 Methodology

The methodology of the tensile coupon testing is primarily based on ASTM D3039. The

tensile coupon samples were cut to widths of 1 inch and lengths of 19 inches. The gage length of

these samples was 9 inches. This was done in order to fit into the Instron machine used for this

test. The testing machine used was an Instron Hdx 1000. The samples were rectangular in shape

and no tabs were affixed to the samples with the exception of Sample 16-4 (Table 3-15). It can

generally be seen that higher strength can be attained by attaching steel tabs to the ends of the

samples where the testing machine grips the sample (ASTM D3039-08) however, no tabs were

affixed to the samples due to time constraints, and because the results of Sample 16-4 (Table

3-15) matched closely with the results from samples without tabs. Load and deflection data were

recorded by the Instron’s onboard data acquisition software. Strain gages were applied to seven

samples in order to obtain an accurate modulus of elasticity value. The modulus of elasticity is

found as the slope of the initial linear portion of the stress-strain curve (generally 15-30 % of the

71

ultimate strain). The speed of testing was 0.15 in/min. A sample (of section PU-12x0.375) is

shown seated in the tension testing machine in Figure 3-30.

Figure 3-30 Tension Test Sample in Instron Machine

3.7.1.2 Results and Discussion

It is important to remember that section PU-16x0.5 and PU-12x0.5 are made up of the

same fiber and resin materials and also have similar layups. Tensile tests were only performed on

sections PU-16x0.5, PU-12x0.5, and PU-12x0.375; therefore, no tests were performed on vinyl

ester specimens. The results are for all sections are shown in the following three tables.

Table 3-15 Coupon Static Tension Test Results - Section PU-16x0.5

Sample Max Load (lbs)

Deflection at Max

Load (in)

Max Stress (psi)

Max Strain

(με)

Elastic Modulus

(Msi)

16-1 50504 0.672 110391 - 6.30 16-2 49460 0.618 95834 - - 16-3 51578 0.667 99938 - - 16-4* 52331 0.552 104079 - -

Average 50968 0.627 102561 - - *16-4 has end tabs affixed

72



Deflection at Max

Load (in)

Max Stress (psi)

Max Strain

(με)

Elastic Modulus

(Msi)

12-1 48846 0.636 94370 - - 12-2 46411 0.658 89944 - - 12-3 51412 0.705 98321 - - 12-4 47008 0.644 92046 - - 12-5 52495 0.656 100621 19198 5.34

Average 49234 0.660 95060 - -



Deflection at Max

Load (in)

Max Stress (psi)

Max Strain

(με)

Elastic Modulus

(Msi)

3-7 41978 0.683 114914 - - 3-5 36776 0.597 98463 - - 3-8 42694 0.658 119357 - - 3-2 38012 0.652 105942 22052 4.861 3-1 34241 0.640 100561 22058 4.658 3-3 40004 0.622 106877 20821 5.112 3-6 37068 0.609 100103 22468 4.560 3-9 42112 0.657 109752 25023 4.658

Average 39111 0.640 106996 22484 4.770

The deflection at max load measurements recorded by the Instron shown above should be

viewed with caution because of the fact that steel tabs were not used. It was noted that after all

the failures the grips were digging into the sample in the grip area during testing. This shows that

some extra deflection, although minor, is occurring throughout the entire test (Note that the

sample with tabs, 16-4, from Table 3-15 shows less deflection than the others). As shown in

Figure 3-31, failure of the samples is more pronounced near the gripped ends which shows that

73

failure may have initiated at the grip edge; although, failure throughout the entire gage length

occurred suddenly. This failure can be seen clearly in Sample 16-4 shown in Figure 3-32.

Figure 3-31 Failed Samples from Tensile Coupon Test

74

Figure 3-32 Coupon Tension Failed with Grips (Sample 16-4)

3.7.2 Bending

3.7.2.1 Methodology

The only section that was tested in coupon bending is PU-12x0.375, the 3/8” thick

polyurethane. This test was done in order to provide more data about the section and allow for

correlation to the full section. Just as was done for the tension tests, bending coupon samples

were cut from the specimens that failed under crushing. The ends of these sections do not appear

to have any damage; however, this is based on a visual inspection. It is not truly known if there

was any internal damage. Nine samples were cut first using a handheld circular saw and then

were cut to size using a table saw both having a diamond blade. The methodology for sample

preparation and test setup is followed from ASTM D790. The samples were cut to widths of 1

inch and lengths of 10 inches. Measurements of each specimen were taken along the gage length

75

in three places with respect to width and thickness and then averaged in order to obtain accurate

flexural strength results. The span length used was 6 inches which corresponds to a span to depth

ratio of 16:1. In order to rule out the possibility of shear deformation effects, an additional

sample with a span length of 9 inches was used (24:1 span to depth ratio). The machine used to

test these samples was an Instron 8800, and a three point bending fixture was used (see Figure

3-34). Load and deflection data were recorded by the Instron’s onboard data acquisition

software. For one sample, a strain gage was installed along the bottom in the center in order to

obtain a modulus of elasticity for comparison to those obtained from the load-deflection curve.

The speed of testing for the 6 inch samples was 0.16 in/min and 0.36 in/min for the 9 inch

sample.


The results of coupons under bending are shown in Table 3-18 and Figure 3-33. A typical

failure is shown in Figure 3-34. All samples failed very similar to the one pictured in Figure

3-34, with failure occurring in the middle under the applied load. It should be noted that the

modulus of elasticity is calculated using the formula given in ASTM D790 for tangent modulus

of elasticity. A strain gage was applied to Sample 3-10 and the modulus from the resulting stress-

strain curve was 3.126 Msi which is 10% higher than the modulus of elasticity obtained from the

load-deflection curve. This indicates that some slippage or other inaccuracy that occurred in the

testing machine which is yielding lower moduli of elasticity based on load-deflection data.

Sample 3-4 was the 9 inch span length specimen. Its results (moment, stress, and modulus) are

close to the average of the other samples. This further conveys that little to no shear strength is

affecting the results.

76

Table 3-18 Coupon Bending Test Results - Section PU-12x0.375

Sample

Max Load (lbs)

Max Moment (lb-in)

Deflection at Max

Load (in)

Max Stress (psi)

Modulus of

Elasticity (Msi)

3-10 1454 2182 0.552 94104 2.843 3-11 1663 2495 0.528 110391 3.465 3-12 1739 2609 0.590 109507 3.207 3-13 1492 2239 0.584 100685 3.018 3-14 1644 2466 0.611 104861 2.975 3-15 1639 2458 0.508 104657 3.256 3-16 1648 2473 0.541 107896 3.511 3-17 1585 2378 0.606 106037 2.973

Average 1608 2412 0.565 104767 3.156

3-4* 1087 2445 1.152 102994 3.313 *Span length on this sample is 9 in.

Figure 3-33 Load/Deflection Response for Coupon Bending Tests - Section PU-12x0.375

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Load

(lbs

)

Deflection (in)

Sample 3_10 Sample 3_11Sample 3_12 Sample 3_13Sample 3_14 Sample 3_15Sample 3_16 Sample 3_17

77

Figure 3-34 Typical Failure for Coupon Bending Tests - Section PU-12x0.375

3.7.3 Compression

3.7.3.1 Methodology

The only section that was tested in coupon compression was PU-12x0.375, the 3/8” thick

polyurethane. These tests were performed in accordance with ASTM D695 Just as was done for

the tension and bending tests, compression coupon samples were cut from the specimens that

failed under crushing. The ends of these sections do not appear to have any damage; however,

this is only speculation from a visual inspection. It is not truly known if there was any internal

damage. Six samples were cut first using a handheld circular saw and then were cut to size using

a table saw both having a diamond blade. The samples were cut to widths of ½ inch and lengths

of 1.75”. The dimensions were chosen in order to remove the chance of buckling behavior and

conform to ASTM D695. Measurements of each specimen were taken along the gage length in

three places with respect to width and thickness and then averaged in order to obtain accurate

78

axial compressive strength results. The same Instron machine was used for the compression tests

as for the bending tests, the Instron 8800; however, two flat hardened and ground plates were

used as fixtures. The bottom plate was a fixture with the ability to rock in any direction. This was

used to ensure the plates would be parallel while compressing the sample. The speed of testing

was 0.05 in/min.


The coupon test results under compression are shown in Table 3-19. A typical failure is

shown in Figure 3-35. All samples failed very similar to the one pictured, with failure occurring

at either the top or bottom of the sample in a crushing manner.

Table 3-19 Coupon Compression Test Results - Section PU-12x0.375


Cross Section Area (in2)

Deflection at Max

Load (in)

Max Stress (psi)

3-21 8739 0.1611 0.065 54246 3-24 9653 0.1715 0.074 56288 3-18 7820 0.1695 0.079 46135 3-23 9961 0.1664 0.082 59861 3-19 9005 0.1656 0.072 54376 3-20 8123 0.1663 0.073 48847

Average 8884 0.1667 0.074 53292

79

Figure 3-35 Typical Failure for Coupon Compression Tests - Section PU-12x0.375

The results from the compression coupon testing in Table 3-19 yield low stresses to failure

when compared to the tensile results in Table 3-17 (about half). This reason for this is possibly

due to the size of the compression samples. Because of using a table saw and circular saw with

relatively large diameter blades (~1/8 in thick) compared to the sample size, damage is likely to

have occurred to the resin and fibers that affected the results. Therefore, it appears these results

should be taken with caution and it is recommended that testing on large samples should be

done.

80

3.8 Four-Point Bending Fatigue

3.8.1 Methodology

One full section sample of sections PU-16x0.5, VE-16x0.5, and PU-12x0.5 was tested in

bending fatigue. Using the same test setup for four-point static bending as described in section

3.3, each sample underwent 200 cycles of approximately 40% of its respective average

maximum load. After the sections were subjected to the 200 cycle fatigue test, they were tested

to failure in static four-point bending fashion as described in section 3.3. It should be noted that a

cycle consisted of roughly a 2 kip minimum load and a maximum load of 40% of the average

failure load of previous samples. The actual loads applied under fatigue were slightly different

and are recorded as shown in Table 3-20. At a rate of loading of 0.075 Hz (cycle/sec), each test

endured 44 minutes to attain 200 cycles. This was chosen because of the MTS fatigue actuator’s

ability to run smoothly at this rate of loading. The machine used was an MTS Teststar Controller

with a maximum compression load of 330 kips. It contains an internal load cell which was

calibrated in February 2011 by MTS. Deflection was measured by a Celesco SP3 string pot.


A summary of the bending fatigue test results is shown in Table 3-20. Within each section

set the last sample was set aside for fatigue, and they are each labeled “S6”. The R-ratio relates

the ratio of the minimum load to maximum load of the fatigue test. It is calculated based on the

results after the test was run. The deflection range shows the average of the difference between

the maximum and minimum deflections experienced during the testing. The goal for load level

was 40%; however, the machine’s ability to attain these loads is restricted by the servo-hydraulic

system. The values shown in Table 3-20 were the actual load levels achieved by the machine.

81

Table 3-20 Four-Point Bending Fatigue Results

Section,

Sample #

Rate (Hz)

R-ratio Load Level (%)

Avg Min Load (kips)

Avg Max Load (kips)

Load Range (kips)

Avg Deflection

Range (in)

Number of Cycles

PU-16x0.5, S6 0.075 0.18 38.0 6.94 38.64 31.70 3.84 200 VE-16x0.5, S6 0.075 0.15 43.9 5.39 36.44 31.05 3.92 200 PU-12x0.5, S6 0.075 0.13 40.0 4.8 36.41 31.61 3.58 200

After the fatigue test of 200 cycles, the samples were tested in static four-point bend to

failure. The results for each of these samples are given earlier in section 3.3.2.

3.9 Cantilever Bending Test

3.9.1 Methodology

One full section of section PU-12x0.375 was tested in cantilever to a load well below

expected failure (8000 lbs) in order to further examine the section. The test setup, shown in

Figure 3-36, uses a full section of 280 inches length, but the member is partially fixed at the

midpoint of the span. A chain link choker is attached to the specimen at a distance of 40 inches

from the end which is connected to a torsion crank. A flaw in this test setup is introduced where

the tube is intended to be fixed. Since the tube extends 140 inches beyond this point in the

direction opposite the loading, it is allowed somewhat to bend therefore not representing true

fixed conditions. In between the crank and the choker a 10 kip S-type tension-compression load

cell was placed. Deflection is measured by a Celesco SP3 string pot directly under the point of

load. Eight strain gages were attached near the fixed point at all locations shown in Figure 3-3.

82

Figure 3-36 Cantilever Bending Test Setup


A summary of the results are presented in Table 3-21. Because this test did not go to failure

of the section, but to the predetermined maximum load of 8.12 kips, the values shown are what

were measured with respect to that maximum load.

Table 3-21 Cantilever Bending Test Results - Section PU-12x0.375

Max Load (kips)

Max Deflection

(in)

Max Moment

(k-in)

Max Stress (ksi)


Elastic Modulus

(Msi)

Energy (kip-in)

8.12 6.78 779 20.19 3601 5.74 25.919

The deflection shown in Table 3-21 is the result of the inability to fully restrain the

specimen at the fixed support. It is much higher than expected. However, the strain

measurements provide more reliable information. The elastic modulus here shows some

83

disagreement with the average modulus obtained from the four-point bend test, 5.26 Msi, which

yields a percent difference of 13.5 %. This is due to the cantilever section only undergoing 33%

of the maximum strain recorded during four-point bending (Table 3-9). The portion of the stress-

strain curve used to calculate this modulus is the initial portion of the would-be entire curve

(15%-33% of the ultimate strain) and is therefore more linear than the portion of the stress-strain

curve used in the four-point bend tests (10%-50% of the ultimate strain).

3.10 Conclusions

The extensive mechanical tests performed on the four different sections provide a wealth of

information about their mechanical behavior. The difference between polyurethane and vinyl

ester resin systems is shown by comparing the results of section PU-16x0.5 and section VE-

16x0.5. From the four-point bending test, the average ultimate bending stress for section PU-

16x0.5 was found to be 59.21 ksi and the elastic modulus was calculated as 5.92 Msi. The

average ultimate bending stress for section VE-16x0.5 was found to be 49.02 ksi and the elastic

modulus was calculated as 5.57 Msi. This is a 17% and 6% drop respectively with relation to

PU-16x0.5. While the two base materials have similar material properties, polyurethane has a

much higher percent strain to failure. This difference in percent strain to failure of the resins is

believed to be the reason why polyurethane withheld higher loads, had a higher stiffness, and

also experience more cross sectional deformation during loading. PU-12x0.5 had an average

ultimate bending stress of 72.94 ksi and an elastic modulus of 6.61 Msi. This section has a

diameter to wall thickness ratio of 24 (D/t = 24) which resulted in less local buckling

contribution to failure and is therefore why this section sustained a higher failure stress than

section PU-16x0.5 (D/t = 32). PU-12x0.375 had an average ultimate bending stress of 55.61 ksi

and an elastic modulus of 5.26 Msi.

84

Surveying the coupon results for sections PU-16x0.5 and PU-12x0.5 shows very similar

results. This is to be expected due to the similarity of the layup. The maximum tensile stress for

these coupons is approximately 100 ksi. When observing the coupon results for tension and

compression for section PU-12x0.375, the max stress for compression is 53.3 ksi and the max

stress for tension is 107.0 ksi. The coupon bending tests for PU-12x0.375 yield an ultimate

bending stress of 103 ksi and an elastic modulus of 3.31 Msi.

In the crush testing, the polyurethane section PU-16x0.5 again outperformed its vinyl ester

counterpart, section VE-160.25, due to the greater ductility of the polyurethane resin system. PU-

16x0.5 boasts a maximum crush loading of 27.53 kips and VE-16x0.5 resulted in a maximum

crush loading of 18.75 kips. PU-12x0.5 and PU-12x0.375 had maximum crush loadings of 27.54

and 18.36 kips, respectively. For connection testing A, flattening of the cross section is a real

possibility as well; however, it presumably would not affect the failure load much. PU-16x0.5

had a failure load of 23-25 kips, and VE-16x0.5 had a failure load of 18-21 kips. Section PU-

12x0.5 had a maximum failure load of 21-23 kips. The PU-12x0.5 showed a ~8% lower failure

load than section PU-16x0.5. This is due to the higher curvature of the wall in the 12” diameter

section, and also probably due to the length of the bolt used across the diameter of the tube.

Connection Test B, the washer test, yielded insight into each section’s ability to withstand a

localized washer load. In every case the washer yielded and failed, but failure loads were

recorded when each section showed initial cracking that ran longitudinally. PU-16x0.5 showed

failure loads of 17.2 and 22.2 kips for the 4 inch and 6 inch washer respectively. VE-16x0.5

showed failure loads of 14.3 and 17.8 kips for the 4 inch and 6 inch washer respectively. PU-

12x0.5 showed failure loads of 19.6 and 27.6 kips for the 4 inch and 6 inch washer respectively.

85

The cantilever bending test performed on PU-12x0.375 resulted in an elastic modulus of 5.74

Msi.

86

CHAPTER 4 BENDING BEHAVIOR PREDICTION OF GFRP

TUBES

4.1 Introduction and Scope

For thin-walled cylindrical sections, designers and engineers need to know as much as

possible about the stiffness behavior, ultimate strength, and susceptibility to buckling geometric

instability. Laminated composites are more complex than metals due to anisotropy and

inhomogeneity not to mention the variety of fiber architectures and resin systems. Therefore

accurate prediction for the mechanical behavior will require material properties of varying

elements and constituents of laminated composites.

Of particular interest is the change in stiffness that occurred during the full-section bending

tests to failure described earlier in the paper (see section 3.3). The results of these tests indicate a

primary failure mode of crushing on the compression face including local buckling. This

behavior will be analyzed in further detail in this section. An attempt is made to define a viable

methodology for predicting the stiffness and ultimate strength of the large diameter thin walled

cylindrical composite tubes that were tested in four-point bending. Finite element analysis is also

used for comparison, particularly in regards to the stiffness.

4.2 Analysis Methodology

In order to quantify the change in flexural stiffness reduction during testing, a graph of the

derivative of the stress-strain curve will be analyzed for each section. This graph is made by

taking the change in stress at intervals of 250 με and dividing by the change in strain (250 με)

throughout the loading. Figure 4-1 and Figure 4-2 show the stiffness change plotted against the

87

percent of ultimate strain in the tension face and compression face, respectively, for Sample 6 of

VE-16x0.5. This sample is representative of all samples of section VE-16x0.5 with the exception

of Sample 1 in which case Sample 1 dropped more dramatically to near 4 Msi at failure.

Figure 4-1 Change in Stiffness Curve from Four-Point Bend Sample 6 (Tension Face) - Section VE-16x0.5

0

1

2

3

4

5

6

7

8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Tens

ion

Stiff

ness

(Msi)

Strain (%)

88

Figure 4-2 Change in Stiffness Curve from Four-Point Bend Sample 6 (Compression Face) - Section VE-16x0.5

The change in stiffness throughout loading for section VE-16x0.5 is generally linear. The

change in stiffness on the compression face and on the tension face is mostly the same. Therefore

with section VE-16x0.5, an exact point where stiffness reduction begins is undeterminable. This

makes clear that local buckling does not contribute much, if any, to stiffness changes in VE-

16x0.5.

Different behavior was found in section PU-16x0.5. While the flexural stiffness reduced

during the test, it reduced in a different fashion than VE-16x0.5. Samples 2, 3 and 5 had a

longitudinal strain gage at the top of the specimen while Samples 1, 4, and 5 had a longitudinal

strain gage on the bottom (Sample 5 had both). There is a difference in the stiffness reduction

based on whether the strain was measured on the top (compression face) or the bottom (tension

face) of the specimen. Figure 4-3 and Figure 4-4 illustrate the flexural stiffness reduction for

sample 5 of section PU-16x0.5 both on the compression face and tension face.

0

1

2

3

4

5

6

7

8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Com

pres

sion

Stiff

ness

(Msi)

Strain (%)

89

Figure 4-3 Change in Stiffness Curve from Four-Point Bend Sample 5 (Compression Face) - Section PU-16x0.5

Figure 4-4 Change in Stiffness Curve from Four-Point Bend Sample 5 (Tension Face) - Section PU-16x0.5

1

2

3

4

5

6

7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Com

pres

sion

Stiff

ness

(Msi)

Strain (%)

1

2

3

4

5

6

7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Com

pres

sion

Stiff

ness

(Msi)

Strain (%)

90

These graphs are both typical of the other samples from this section set. Consistently, the

bottom stiffness change (Figure 4-4) follows a less dramatic reduction while the top stiffness

change (Figure 4-3) experiences a drastic change. This is because local buckling occurs on the

compression face of the specimens. From 0-45% strain the stiffness is fairly constant and then

from 45-100%, the stiffness takes on a linear decrease with increase in strain. At around 45% of

ultimate strain change in slope begins to occur in the specimen and the cross section starts

deforming. To back up this claim, the stiffness change for sample 2 (gage located at top) is

shown in Figure 4-5.


As shown in Figure 4-5, the stiffness change also follows a two-part pattern. From 0-40%

strain the stiffness is fairly constant and then from 40-100%, the stiffness takes on a linear

decrease. The same sample was discussed earlier in section 3.3.2.2 and it was decided, based on

circumferential strain on the side of the tube that nonlinearity began at 40% of the ultimate load.

The same conclusion can be made here for 40% of ultimate strain. This matches closely with the

1

2

3

4

5

6

7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Com

pres

sion

Stiff

ness

(Msi)

Strain (%)

91

sample 5 results in which ~45% of ultimate strain was the bifurcation point. Although not shown

here, sample 4 having a gage on the tension face, shows strikingly similar behavior as sample 5

(Figure 4-4). Sample 4 changes from a constant stiffness to a decreasing linear stiffness at around

40% of ultimate strain.

Section PU-12x0.5, with a D/t ratio of 24, exhibits similar behavior to the previously

discussed sections. Two of the five sections had strain gages on the top in the longitudinal

direction and the other three had strain gages on the bottom in the longitudinal direction. As with

the section PU-16x0.5, the top strain gage shows a two part stiffness curve in which a constant

stiffness characterizes the tube up to a certain strain, and then a decreasing linear change occurs.

The tubes that had the longitudinal gage on the bottom (tension face) convey a linearly

decreasing change throughout the entire loading. Evidence for this claim can be seen in Figure

4-6 and Figure 4-7, which show the compression strain gage and the tension strain gage,

respectively for two different samples.

92



Similar to previous sections, section PU-12x0.5 shows a point at which the stiffness begins

changing. As seen in Figure 4-6, this point is roughly 57% of the ultimate strain. Also, for the

other sample with a compression face strain gage from section PU-12x0.5, the stiffness change

3

3.5

4

4.5

5

5.5

6

6.5

7

7.5

8

0 0.2 0.4 0.6 0.8 1

Com

pres

sion

Stiff

ness

(Msi)

Strain (%)

3

3.5

4

4.5

5

5.5

6

6.5

7

7.5

0 0.2 0.4 0.6 0.8 1

Tens

ion

Stiff

ness

(Msi)

Strain (%)

93

occurs at approximately 50% of the ultimate strain. Both of these are higher than the 40-45% of

ultimate strain at which the stiffness changed for section PU-16x0.5.

Section PU-12x0.375, having a D/t ratio of 32, showed the least amount of stiffness

reduction throughout loading compared to the other specimens. All three specimens had the

longitudinal strain gage located on the bottom of the tube; however, the post-fatigue sample had

a strain at both top and bottom locations. It was decided earlier (section 3.8) that the 200 fatigue

cycles had little to no effect on the stiffness and strength of the tube; therefore, this tube will be

examined to determine how the stiffness changes during loading. Figure 4-8 and Figure 4-9

illustrate the change in stiffness as recorded from the top (compression face) and bottom (tension

face), respectively, of sample 4 of section PU-12x0.375.


2

2.5

3

3.5

4

4.5

5

5.5

6

0 0.2 0.4 0.6 0.8 1

Com

pres

sion

Stiff

ness

(Msi)

Strain (%)

94


Figure 4-8, showing the change in stiffness with respect to the compression face, shows

vague correlation the results of the previously discussed sections. The change in stiffness occurs

in two parts; although, the change is less dramatic than the other sections. This is probably

attributed to a higher percent of non-unidirectional fibers. Section PU-12x0.375 contains the

same +45/90/-45 fiber mat as the other sections; therefore, since the wall thickness of section

PU-12x0.375 is less than the other sections the non-unidirectional fiber mat plays a large role in

resisting any cross sectional deformation. The change from constant stiffness to linear decreasing

stiffness occurs at approximately 50% of ultimate strain. Figure 4-9 illustrates that the tension

face of the tube doesn’t experience the same stiffness reduction behavior, but instead the

stiffness drops somewhat linearly throughout the loading.

From the stiffness analysis of all four sections, a bilinear change was found on the

compression face of the tubes. This bilinear change in stiffness did not occur clearly for VE-

2

2.5

3

3.5

4

4.5

5

5.5

6

0 0.2 0.4 0.6 0.8 1

Ten

sion

Stif

fnes

s (M

si)

Strain (%)

95

16x0.5; however, it occurred at approximately 40% strain for PU-16x0.5, 50-55% strain for PU-

12x0.5, and 50% for PU-12x0.375. These results are summarized in Table 4-1 along with the D/t

ratio for each section. This is shown in order to emphasize that a higher D/t results in an earlier

onset of nonlinearity during bending.

Table 4-1 Summary of Stiffness Change Points

Section D/t Stiffness Change (% of ultimate

strain)

Stiffness Change (% of ultimate

stress)

PU-16x0.5 32 40 44 VE-16x0.5 32 N/A N/A PU-12x0.5 24 50-55 58-60

PU-12x0.375 32 50 50

4.3 Bending Stiffness Replacement - Laminated Plate Approach

A method to determine bending stiffness, EI, for a cylindrical section based on classical

lamination theory (CLT) is explained below. This bending stiffness can be used as a replacement

in designer friendly bending equations such as Euler-Bernoulli’s equation. As it applies to the

bilinear stiffness experienced by the tubes tested in four-point bending, this replacement stiffness

will yield a comparable result to the initial constant stiffness before the bifurcation. Using the

manufacturer-supplied fiber architecture and material properties, laminate properties can be

found with reasonable accuracy by the rule of mixtures approach (Barbero, 2011). The raw

material properties were given by the manufacturer; however, some had to be approximated

using published data. The raw material properties used are shown in Table 4-2.

96

Table 4-2 Raw Material Properties used in Tube Sections

Material Elastic Modulus

Tensile Strength

% Elongation to failure

Poisson's Ratio

Density Compression Strength

Shear Strength

Shear Modulus

(psi) (psi) % (lb/in3) (psi) (psi) (psi)

E-glass 11000000 325000 4.4* 0.22* 0.0919 - 4508197* VE 464121 12473 5.5 0.38* - 16984* 11995* 168160*

PUR 420609 12038 9.4 0.41 - - 8100

*This value was taken from Barbero (2011).

The modulus in the fiber direction and the main Poisson’s ratio were found by Equations

4-1 and 4-2:

𝐸1 = 𝑉𝑓𝐸𝑓 + 𝑉𝑚𝐸𝑚 (4-1)

𝜈12 = 𝑉𝑓𝜈𝑓 + 𝑉𝑚𝜈𝑚 (4-2)

where Ef and Em are the Young’s moduli, Vf and Vm are the volume fractions, and νf and νm are

the Poisson’s ratios for the fibers and matrix, respectively. The transverse modulus is better

approximated using the Halpin-Tsai formula shown in Equation 4-3:

𝐸2 = 𝐸𝑚 �1 + Ϛ𝜂𝑉𝑓1 − 𝜂𝑉𝑓

� (4-3)

𝜂 =𝐸𝑓 𝐸𝑚⁄ − 1𝐸𝑓 𝐸𝑚⁄ + Ϛ

where the value Ϛ = 2 is a good fit for the case of circular fibers (Barbero, 2011). The shear

modulus is found by the cylindrical assemblage model as shown in Equation 4-4

𝐺12 =�1 + 𝑉𝑓� + �1 − 𝑉𝑓�𝐺𝑚/𝐺𝑓�1 − 𝑉𝑓� + �1 + 𝑉𝑓�𝐺𝑚/𝐺𝑓

(4-4)

where Gf and Gm are the shear moduli for the fibers and matrix, respectively.

97

Once the moduli are obtained for each lamina and the [ABD] matrix is calculated for a

laminated plate, then the stiffness replacement for a closed tubular section can be found by

Equation 4-5, derived by Kollár (Kollár & Springer, 2003):

𝐸𝐼�𝑦𝑦 = ��1𝑎11

𝑧2 +1𝑑11

cos2 𝛼�(𝑆)

𝑑𝜂 (4-5)

Equation 4-5 is valid for a symmetric and orthotropic layup and may be modified for

cylindrical sections as shown in Equation 4-6:

𝐸𝐼�𝑦𝑦 = 𝐸𝐼�𝑧𝑧 = 𝜋 �𝑅3

𝑎11+

𝑅𝑑11

� (4-6)

Once the replacement stiffnesses are obtained from Equation 4-6, they can be directly

compared to moduli values calculated from experimental bending testing (see section 3.3.2). The

comparison of the theoretical bending stiffness to the experimental bending stiffness is shown in

Table 4-3 with the percent difference showing the theoretical values deviation from experiment.

This method resulting in Equation 4-6 will hereafter be referred to as CLT for convenience.

Table 4-3 Bending Stiffness Comparison, CLT vs. Experiment

Section Bending Stiffness, EI (Mlb-in2) Percent

Difference Experiment CLT PU-16x0.5 4333 3770 -12.99 VE-16x0.5 4077 3813 -6.47 PU-12x0.5 1978 1570 -20.61

PU-12x0.375 1218 1181 -3.04

Also calculated using theoretical bending stiffness were center span deflections through

Euler – Bernoulli’s beam deflection equation at the center span for four-point bending:

𝛥 = 𝑃𝐿3

28𝐸𝐼 (4-7)

98

The deflections found from Equation 4-7 for each section were from 10-30 % higher than

the experimental values. This can be observed in the following load deflection curves (Figure

4-11 through Figure 4-14). It isn’t completely clear why the theoretical deflections are lower

than the experimental deflections, but since the CLT and the FE results match closely, it is likely

due to small discrepancies between the material properties and fiber architectures used in the

theoretical calculations and the true characteristics of the sections.

4.4 Failure Load Prediction

As discussed in the Literature Review (CHAPTER 2), there are many equations available

for determining the critical moment that causes collapse of a thin walled composite tube.

However, for the tubes tested in the study, the failure mode from four-point bending resulted in

crushing under axial compression resulting in local buckling. Therefore, the equations presented

in the Literature Review in section 2.3 (Equations 2-3 through 2-14) are only valid whenever

local buckling is the cause of failure.

In order to predict the failure load of the tubes in bending, the additional local buckling

must be accounted for with the bending stress. Using the failure strain as the criteria for

determining when the tubes will fail, the global bending strain is calculated as follows

𝑀𝑐𝐸𝐼

= 𝜀 (4-8)

where M is the applied bending moment, c is the distance from the centroid to the outermost

fiber of the tube, E is the Young’s Modulus in the axial direction, and I is the moment of inertia

of the tube. This is the commonly used Euler equation for bending stress; however, to account

99

for additional load due to local buckling, an axial load compression effect will be added to the

bending stress resulting in

𝑀𝑐𝐸𝐼

+𝑃𝐴

= 𝜀 (4-9)

where P is the load either of the application points, and A is the area of the cross section in

compression. By inspection, A will be no greater than half the cross sectional area; however, it

can be adjusted to fit the properties of the tube. Substituting PL/3 for M to fit the case of four-

point bending and rearranging to solve for P results in

𝑃 =𝐸𝜀

�𝐿3𝑐𝐼 + 1

𝐴� (4-10)

where L is the span length. Generally speaking, the top half of the cylinder is in compression;

therefore, A will be taken as half of the cross sectional area of each tube. Using the average

modulus and average maximum strain from the four-point bending experimental tests, the failure

load, P, was calculated. The results of Equation 4-10 compared to the experimental failure load

are shown in Table 4-4. Also included in Table 4-4 is the result of the equation ignoring the local

compression effect (Equation 4-8).

Table 4-4 Failure Load Prediction Compared to Experiment

Accounting for P/A Effect

Ignoring P/A

Section Max Load (kips)

Avg Max Strain

(με)

2P (Eq 4-10) (kips)

% Difference

2P (Mc/I) (kips)

% Difference

PU-16x0.5 101.63 11152 105.80 4.10 113.26 11.44 VE-16x0.5 83.06 8913 79.56 -4.21 85.17 2.54 PU-12x0.5 90.93 12720 98.05 7.83 104.81 15.27

PU-12x0.375 52.98 10843 51.41 -2.96 55.04 3.88

100

As shown in Table 4-4, accounting for the local compression effect yields a more accurate result

compared to experiment that ignoring this effect. Equation 4-10 produces better correlation in

every section with exception of VE-16x0.5 which was noted earlier to not experience much, if

any, local buckling effect.

4.5 Finite element Analysis

The four-point bending tests were modeled using finite element analysis to further

characterize the local buckling behavior that occurs during loading.

Using the rule of mixture equations (Equations 4-1 through 4-3), the material properties

were defined for each lamina. ANSYS software was used for the finite element modeling. A

four-node element with six degrees of freedom at each node was used; using this element, any

number of lamina can be defined for each section. The 16 in diameter tubes, PU-16x0.5 and VE-

16x0.5, were both discretized with 28 elements in the circumferential direction and 160 elements

in the longitudinal direction. The 12 in diameter tubes, PU-12x0.5 and PU-12x0.375, were both

discretized with 20 elements in the circumferential direction and 120 elements in the longitudinal

direction. Figure 4-10 depicts a 16” diameter tube discretized with boundary conditions and

external loads. The red arrows are the applied load which match the location of the experiment,

and the light blue represent the boundary conditions. The tube was restricted in Y and X

directions at the end and in the Z direction at center span. The Y and X restrictions mimic the

experimental setup; however, the Z restraint was added in order make the model stable.

101

Figure 4-10 Discretized Tube Modeled in ANSYS with External Loads and Boundary Conditions

After running the model in a linear static mode, results were found to be nearly identical to

those obtained by CLT. In order to account for the change in shape of the cross section that

occurs during bending and the resulting stiffness reduction, a large displacement mode was used.

This mode uses the Newton-Raphson method to converge on a solution. As the load is broken

down into steps, ANSYS adjusts the stiffness matrix of each step to reflect any geometric

changes in the cross section.

The maximum load reached in the experiment was set as the max load in the model,

leaving the model to automatically choose time steps as it ramped up to the input maximum. The

resulting loads vs. deflections plots from the finite element analysis are shown for each section in

the following figures (Figure 4-11 through Figure 4-14).

102


Figure 4-12 Load-Deflection Curve Comparison for Exp vs. FEM vs. CLT - Section VE-16x0.5

103



Each model produced results almost exact to that of the CLT prediction, and for each

section with the exception of PU-12x0.5, the deflections were anywhere from 10% to 18%

different than experiment. Section PU-12x0.5 was approximately 20% to 30% under predicting.

104

It is not completely clear why the FEM was consistently underpredicting. Since the FEM

matches so closely with the CLT theory deflection results, it is assumed that accurate material

properties or layup architecture were not used.

In order to validate whether the finite element was able to capture the cross sectional

deformation accurately, the reduction in vertical radius of the cross section is observed from the

finite element model. A technique taken from Ibrahim et al. (2000) was applied to the previously

developed FE models. By subtracting the bottom deflection from the top deflection at midspan,

the change in vertical radius was found. The result of this is then compared to experimental

results. Video footage was conducted on Sample 4 of PU-12x0.375 and the change in vertical

radius was observed from the footage. The results of the finite model and experimentation are

shown and compared in Figure 4-15.

105

Figure 4-15 Ovalization Comparison of Finite Results vs. Experimental Results

Figure 4-15 depicts the resulting FE ovalization ratios and corresponding load ratios for

sections PU-16x0.5 and PU-12x0.375, where Ro is the initial radius of the cross section and U is

the radial deformation distance. Loading is not shown up to the max experimental load for the

FE models because instability was reached in the model before that point. The finite model

slightly provides a good approximation of ovalization.

4.6 Conclusion

From the four-point bending tests, sections PU-16x0.5, PU-12x0.5, and PU-12x0.375 were

shown to have a bilinear stiffness behavior. The stiffness remains constant up to a certain

strain/load and then began to decrease linearly. Section VE-16x0.5 showed a more stable

stiffness and only decreased slightly throughout loading. The reason for this is due

polyurethane’s ductility and high strain to failure as shown in Table 4-2. PU-16x0.5 experienced

a stiffness change at 40% strain for PU-16x0.5, 50-55% strain for PU-12x0.5, and 50% for PU-

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 0.02 0.04 0.06 0.08 0.1

Rat

io o

f Loa

d to

Max

Exp

Loa

d

Ovalization Ratio (U/Ro) at Mid-Span

FEA: PU-16x0.5

FEA: PU-12x0.375

Exp: PU-12x0.375

2Ro-2U

106

12x0.375. PU-12x0.5 experienced a stiffness change at a higher percentage due to its higher D/t

ratio. A good scientific reason for the stiffness changing and local buckling occurring at certain

percentages of ultimate strain is unknown; however, the tests do show and describe this behavior

and therefore it is likely caused by compression of the fibers as described.

A bending stiffness prediction was made based on classical lamination theory. The results

showed an underprediction for each section. The difference was 13% for PU-16x0.5, 6.5 % for

VE-16x0.5, 20.6 % for PU-120x0.5, and 3% for section PU-12x0.375. The varying differences

are concluded to be somewhat due to inconsistencies from the material properties and fiber

architecture used. Local effects could also yield higher experimental stiffnesses. Deflections

were calculated using Euler’s beam equation for bending and plotted in a load deflection curve.

Finite element modeling was also used to attempt to capture any nonlinear behavior due to local

buckling. The CLT and FEM results were very close until the later loading stages in which the

finite element model loses stiffness as a result of its accounting for nonlinear behavior. For

sections PU-16x0.5, VE-16x0.5, and PU-12x0375 the deflections estimated by CLT and FEM

erred by approximately 10-18 %. For section PU-12x0.5 the CLT and FEM deflections were

underestimated by 20-30 %. Again, since both methods produced similar values, the error

between their prediction and the experimental results most likely lies with assumptions regarding

the material characteristics.

A method is proposed for predicting the failure load. This method attempts to take into

account the local compression effect experience by the tubes in bending. Using the strain and

modulus obtained from experiment, a prediction for each section is made. The failure load

estimation has a percent difference compared to experimental results of +4.1% for PU-16x0.5, -

4.2% for VE-16x0.5, +7.8% for PU-12x0.5, and -2.9%. The results prove to be more accurate

107

than when this effect is ignored. The only section where accounting for the local compression

effect proves to be less accurate is VE-16x0.5. This section is the only section using a vinyl ester

resin, and this section was shown to not experience as much of a contribution from local

buckling/compression from experiment. Therefore, the model predicts well for the sections with

a polyurethane resin system. Additional work should be completed to test this simple approach’s

ability to estimate the failure load of composite tubes in bending, particularly with varying tubes

of different fiber-resin systems and fiber layup architectures.

108

CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS

In this study, a review of published literature was conducted focusing on the following: 1)

bending response of thin-walled cylindrical FRP and steel tubes; 2) plastic bending collapse of

metals; 3) prebuckling response of cylindrical composite tubes; 4) bending stiffness predictions

of composite tubes. A variety of mechanical tests were conducted on four different GFRP

cylindrical tubular sections with varying cross section dimensions and resin systems. The GFRP

tubes, manufactured through pultrusion under high pressure, were tested under bending, local

crushing, and for special joining mechanisms. The test procedures and results are reported in

Chapters 3 and 4, respectively. The polyurethane as well as vinyl ester matrix systems were

tested for load to failure, strain to failure, stiffness, and energy absorption. Using the four-point

bending experimental results, a prediction model is formulated for the failure load of the FRP

tubes, including local compression effects. Good correlation is found with the proposed

prediction technique and the experimental data. As narrated below, specific conclusions on

bending and connection responses are drawn from the experimental and theoretical data.

5.1 Mechanical Testing of Glass FRP Tubes

5.1.1 Four-Point Bending Response

The primary failure mode of all sections under four-point bending was crushing in the

compression side resulting from local buckling. VE-16x0.5 showed minimal local buckling and

exhibited mostly compression crushing failure. The PU-12x0.5 specimens were found to have

much higher stresses and strains to failure than the tubes with higher wall thickness ratios,

indicating that the local buckling effects were more predominant in pipes with relatively thinner

walls (refer to Section 3.3.2). This was evident in the diameter to wall thickness (D/t) ratio being

109

24 for PU-12x0.5 versus 32 for all other samples. Also revealed by the four-point bending

results, was a bilinear stiffness response. The bending stiffness for all polyurethane sections

remained constant up to a certain strain level and then decreased approximately linearly. The

percentage of ultimate strain at which this occurred was approximately 40% for PU-16x0.5, 50-

55% for PU-12x0.5, and 50% for PU-12x0.375 (see Table 4-1). The vinyl ester matrix did not

exhibit such bilinear behavior.

The 200 cycle at 40% of ultimate stress fatigue test showed a negligible stiffness change for

each section except PU-12x0.5 which showed a decrease of 12%. This could be a cause for

concern for designers and it is recommended another test be performed to ensure that fatigue is

not a problem for this section. Section VE-12x0.5 failed at the load saddle during the post-

fatigue static test instead of the center span, this was likely not due to fatigue, but probably an

unsymmetrical loading.

5.1.2 Connection and Coupon Response

The primary failure mode of connection test A was local crushing of the tube wall (refer to

section 3.5.2). The bolt pushed its way through the wall slowly without abruptly rupturing.

Connection test B showed sudden local cracking failure of each section (refer to section 3.6.2).

The 6x6” washer under a point load yielded less local damage than the 4x4” washer due to the

load spread over a larger area.

Tensile coupon testing for section PU-16x0.5 and PU-12x0.5 yielded similar stresses to

failure of 103 and 95 ksi, respectively. The primary mode of failure was fiber breakage at the

grips resulting in delamination. Section PU-12x0.375 experienced similar results with stresses to

failure of 107 ksi. PU-12x0.375 coupons had an average compression failure stress of 53 ksi and

110

an average bending failure stress of 105 ksi. The unusually low compression stress is likely due

to damage to the coupons from cutting.

5.1.3 Comparison of Polyurethane vs. Vinyl Ester

From the four-point bending test, PU-16x0.5 compared to VE-16x0.5 had a 17% higher

load to failure, 20% higher strain to failure, 6% higher elastic modulus, and 38% higher energy

absorbed to failure. From the crush test, the PU-16x0.5 had a 32% higher load to failure.

Although vinyl ester has a higher modulus and tensile strength, polyurethane has a much higher

percent elongation to failure (see Table 4-2). These test results show that polyurethane has a

better bond with the glass fibers. Connection test A revealed that VE-16x0.5 had approximately a

25% lower load to failure. This connection test reveals the higher stiffness of the polyurethane

resin as this test resulted in highly local failure, and therefore highly depends on the resin’s

properties. This could also reveal that the polyurethane is able to bond to the glass fibers as

polyurethane is not inherently stiffer than vinyl ester in raw form (see Table 4-2).

5.2 Theoretical Calculations

5.2.1 Theoretical vs. Experimental Data Comparison

Classical prediction techniques involving lamination theory produced a single bending

stiffness which can be quite useful for designers, but experiments showed that a bilinear stress-

strain curve results from bending tests whenever sections with high D/t ratios reach high strains.

This prediction of bending stiffness is about 3-20% below the experimental results. In these

cases, other techniques must be used to account for the stiffness reduction. A finite element

model can be used to incorporate non-linearity, but is not inherently more accurate than the

classical lamination theory. Finite element modeling can also give insight into the change of

111

shape of thin-walled cylindrical beams, and correlates fairly well in this regard with data

obtained from experimentation.

A simple approach to predicting the failure load of composite tubes undergoing bending was

presented. This approach accounted for the local buckling/compression effect of each section.

The result of this designer friendly approach produced good correlation to experimental results

with errors of +4.1% for PU-16x0.5, -4.2% for VE-16x0.5, +7.8% for PU-12x0.5, and -2.9%.

These errors were lower than the errors resulting from conventional bending stress calculations

with the exception of the vinyl ester section. The results presented in this paper will be used in

upcoming work aimed at equipping designers with equations that can handle stiffness changes

due to the ovalization that occurs in the bending of cylindrical orthotropic tubes.

5.3 Recommendations

In order to reinforce the conclusions presented in this paper, further work comparing

polyurethane to other resin systems should be done. It may be that the pultrusion process is what

allows polyurethane to work better than vinyl ester with glass fibers. Scanning electron

microscope investigation would be useful to obtain greater details of the bond between glass

fibers and polyurethane of tested samples. Simple mechanical tests such as coupon testing with

only unidirectional fibers will eliminate other variables and allow more insight into how well

polyurethane bonds with glass fibers compared to vinyl ester.

The ability of classical lamination theory had some difficulty predicting the stiffness of the

composite tubes. This standard approach typically has better results (Chan & Demirhan, 2000),

but the uncertainty of raw material properties and fiber volume fraction are possible reasons for

112

poorer estimation. The local effect probably has an effect on stiffness; hence more work needs to

be performed on samples made of pultrusion using high pressure resin infusion in order to

confirm the ability of laminate plate theory and predict the bending stiffness. The future work

would ideally consist of simple varying fiber layups (more or less off-axis fibers) and varying

D/t ratio to pinpoint the primary contributor of local compression effects.

Even though, the proposed failure load prediction expression agreed well with

experimental results accounting for the local compression/buckling effects, it would be ideal to

apply the same approach to other composite tubes with varying D/t ratios and fiber-resin

systems. Accounting for the local compression was shown to be better than ignoring it for all

sections except vinyl ester. This recommendation shows that special care needs to be taken when

using the ductile polyurethane resin. Additional work should focus on modifying the failure load

prediction based on material properties of the section such as fiber volume fraction, elastic

moduli, Poisson’s ratio, etc. This would increase the versatility of the model by being able to

adjust for any FRP composite section.

113

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